chapter 3 -...
TRANSCRIPT
![Page 1: CHAPTER 3 - migomendoza.weebly.commigomendoza.weebly.com/uploads/5/4/7/4/54745209/compound_interest... · CHAPTER 3 Compound Interest. ... Example 3.1: If P2,000.00 is invested at](https://reader030.vdocument.in/reader030/viewer/2022040211/5e718ae20ecf311a367d6253/html5/thumbnails/1.jpg)
CHAPTER 3Compound Interest
![Page 2: CHAPTER 3 - migomendoza.weebly.commigomendoza.weebly.com/uploads/5/4/7/4/54745209/compound_interest... · CHAPTER 3 Compound Interest. ... Example 3.1: If P2,000.00 is invested at](https://reader030.vdocument.in/reader030/viewer/2022040211/5e718ae20ecf311a367d6253/html5/thumbnails/2.jpg)
Recall…◦What can you say to the
amount of interest
earned in simple
interest?
![Page 3: CHAPTER 3 - migomendoza.weebly.commigomendoza.weebly.com/uploads/5/4/7/4/54745209/compound_interest... · CHAPTER 3 Compound Interest. ... Example 3.1: If P2,000.00 is invested at](https://reader030.vdocument.in/reader030/viewer/2022040211/5e718ae20ecf311a367d6253/html5/thumbnails/3.jpg)
Do you know?
◦An interest can also
earn an interest?
![Page 4: CHAPTER 3 - migomendoza.weebly.commigomendoza.weebly.com/uploads/5/4/7/4/54745209/compound_interest... · CHAPTER 3 Compound Interest. ... Example 3.1: If P2,000.00 is invested at](https://reader030.vdocument.in/reader030/viewer/2022040211/5e718ae20ecf311a367d6253/html5/thumbnails/4.jpg)
Compound Interest
◦Whenever a simple interest is
added to the principal at regular
intervals, and the sum become
the new principal, the interest is
said to be compounded.
![Page 5: CHAPTER 3 - migomendoza.weebly.commigomendoza.weebly.com/uploads/5/4/7/4/54745209/compound_interest... · CHAPTER 3 Compound Interest. ... Example 3.1: If P2,000.00 is invested at](https://reader030.vdocument.in/reader030/viewer/2022040211/5e718ae20ecf311a367d6253/html5/thumbnails/5.jpg)
Challenge:
◦Give me an example of a
business transaction which
involves compounding or
compound interest.
![Page 6: CHAPTER 3 - migomendoza.weebly.commigomendoza.weebly.com/uploads/5/4/7/4/54745209/compound_interest... · CHAPTER 3 Compound Interest. ... Example 3.1: If P2,000.00 is invested at](https://reader030.vdocument.in/reader030/viewer/2022040211/5e718ae20ecf311a367d6253/html5/thumbnails/6.jpg)
Do you know?
◦Most savings accounts
pay compounded
interest every three
months or quarterly.
![Page 7: CHAPTER 3 - migomendoza.weebly.commigomendoza.weebly.com/uploads/5/4/7/4/54745209/compound_interest... · CHAPTER 3 Compound Interest. ... Example 3.1: If P2,000.00 is invested at](https://reader030.vdocument.in/reader030/viewer/2022040211/5e718ae20ecf311a367d6253/html5/thumbnails/7.jpg)
Therefore,
◦Adding interest to the
principal gives more
interest.
![Page 8: CHAPTER 3 - migomendoza.weebly.commigomendoza.weebly.com/uploads/5/4/7/4/54745209/compound_interest... · CHAPTER 3 Compound Interest. ... Example 3.1: If P2,000.00 is invested at](https://reader030.vdocument.in/reader030/viewer/2022040211/5e718ae20ecf311a367d6253/html5/thumbnails/8.jpg)
Compounded
◦Whenever we encounter the
word “compounded” what we
mean is that “the interest is
added to the principal to have a
new principal.”
![Page 9: CHAPTER 3 - migomendoza.weebly.commigomendoza.weebly.com/uploads/5/4/7/4/54745209/compound_interest... · CHAPTER 3 Compound Interest. ... Example 3.1: If P2,000.00 is invested at](https://reader030.vdocument.in/reader030/viewer/2022040211/5e718ae20ecf311a367d6253/html5/thumbnails/9.jpg)
Something to think about…
◦How does the
interest become
compounded?
![Page 10: CHAPTER 3 - migomendoza.weebly.commigomendoza.weebly.com/uploads/5/4/7/4/54745209/compound_interest... · CHAPTER 3 Compound Interest. ... Example 3.1: If P2,000.00 is invested at](https://reader030.vdocument.in/reader030/viewer/2022040211/5e718ae20ecf311a367d6253/html5/thumbnails/10.jpg)
Compound Amount
◦The final amount at the
end of the term. We will
denote this using
majuscule letter S.
![Page 11: CHAPTER 3 - migomendoza.weebly.commigomendoza.weebly.com/uploads/5/4/7/4/54745209/compound_interest... · CHAPTER 3 Compound Interest. ... Example 3.1: If P2,000.00 is invested at](https://reader030.vdocument.in/reader030/viewer/2022040211/5e718ae20ecf311a367d6253/html5/thumbnails/11.jpg)
Compound Interest
◦It refers to the difference
between the compound
amount S and the original
Principal P.
![Page 12: CHAPTER 3 - migomendoza.weebly.commigomendoza.weebly.com/uploads/5/4/7/4/54745209/compound_interest... · CHAPTER 3 Compound Interest. ... Example 3.1: If P2,000.00 is invested at](https://reader030.vdocument.in/reader030/viewer/2022040211/5e718ae20ecf311a367d6253/html5/thumbnails/12.jpg)
Example 3.1:◦If P2,000.00 is invested at
an interest rate of 8%
compounded annually for 3
years, find the compound
amount and interest.
![Page 13: CHAPTER 3 - migomendoza.weebly.commigomendoza.weebly.com/uploads/5/4/7/4/54745209/compound_interest... · CHAPTER 3 Compound Interest. ... Example 3.1: If P2,000.00 is invested at](https://reader030.vdocument.in/reader030/viewer/2022040211/5e718ae20ecf311a367d6253/html5/thumbnails/13.jpg)
Final Answer:
◦The compound amount in
3 years is P2,519.42 and
the compound interest is
P519.42.
![Page 14: CHAPTER 3 - migomendoza.weebly.commigomendoza.weebly.com/uploads/5/4/7/4/54745209/compound_interest... · CHAPTER 3 Compound Interest. ... Example 3.1: If P2,000.00 is invested at](https://reader030.vdocument.in/reader030/viewer/2022040211/5e718ae20ecf311a367d6253/html5/thumbnails/14.jpg)
Example 3.2:◦Find the compound amount
and compound interest if
P5,000.00 is invested at 10%
compounded semi-annually
for 2 years.
![Page 15: CHAPTER 3 - migomendoza.weebly.commigomendoza.weebly.com/uploads/5/4/7/4/54745209/compound_interest... · CHAPTER 3 Compound Interest. ... Example 3.1: If P2,000.00 is invested at](https://reader030.vdocument.in/reader030/viewer/2022040211/5e718ae20ecf311a367d6253/html5/thumbnails/15.jpg)
Compounded Semi-annually
◦It means the interest earned
in 6 months is added to the
principal to earn additional
interest for the next 6
months.
![Page 16: CHAPTER 3 - migomendoza.weebly.commigomendoza.weebly.com/uploads/5/4/7/4/54745209/compound_interest... · CHAPTER 3 Compound Interest. ... Example 3.1: If P2,000.00 is invested at](https://reader030.vdocument.in/reader030/viewer/2022040211/5e718ae20ecf311a367d6253/html5/thumbnails/16.jpg)
Therefore…
◦Since we’re just finding for
the interest for 6 months we
will divide the rate of interest
by 2.
![Page 17: CHAPTER 3 - migomendoza.weebly.commigomendoza.weebly.com/uploads/5/4/7/4/54745209/compound_interest... · CHAPTER 3 Compound Interest. ... Example 3.1: If P2,000.00 is invested at](https://reader030.vdocument.in/reader030/viewer/2022040211/5e718ae20ecf311a367d6253/html5/thumbnails/17.jpg)
Final Answer:◦The compound amount semi-
annually for 2 years is
P6,077.53 and the
compound interest is
P1,077.53.
![Page 18: CHAPTER 3 - migomendoza.weebly.commigomendoza.weebly.com/uploads/5/4/7/4/54745209/compound_interest... · CHAPTER 3 Compound Interest. ... Example 3.1: If P2,000.00 is invested at](https://reader030.vdocument.in/reader030/viewer/2022040211/5e718ae20ecf311a367d6253/html5/thumbnails/18.jpg)
Reflect:◦How do you find the process
of computing for the
compound amount and
compound interest?
![Page 19: CHAPTER 3 - migomendoza.weebly.commigomendoza.weebly.com/uploads/5/4/7/4/54745209/compound_interest... · CHAPTER 3 Compound Interest. ... Example 3.1: If P2,000.00 is invested at](https://reader030.vdocument.in/reader030/viewer/2022040211/5e718ae20ecf311a367d6253/html5/thumbnails/19.jpg)
◦YAS! I feel
you! It’s very
TEDIOUS!!!!!!
![Page 20: CHAPTER 3 - migomendoza.weebly.commigomendoza.weebly.com/uploads/5/4/7/4/54745209/compound_interest... · CHAPTER 3 Compound Interest. ... Example 3.1: If P2,000.00 is invested at](https://reader030.vdocument.in/reader030/viewer/2022040211/5e718ae20ecf311a367d6253/html5/thumbnails/20.jpg)
LESSON 3.2Finding the Compound Amount and Compound Interest Using
the Formula
![Page 21: CHAPTER 3 - migomendoza.weebly.commigomendoza.weebly.com/uploads/5/4/7/4/54745209/compound_interest... · CHAPTER 3 Compound Interest. ... Example 3.1: If P2,000.00 is invested at](https://reader030.vdocument.in/reader030/viewer/2022040211/5e718ae20ecf311a367d6253/html5/thumbnails/21.jpg)
Example 3.3
◦Find the accumulated value
of P5,000.00 in 4 years if it
is invested at 12%
compounded quarterly.
![Page 22: CHAPTER 3 - migomendoza.weebly.commigomendoza.weebly.com/uploads/5/4/7/4/54745209/compound_interest... · CHAPTER 3 Compound Interest. ... Example 3.1: If P2,000.00 is invested at](https://reader030.vdocument.in/reader030/viewer/2022040211/5e718ae20ecf311a367d6253/html5/thumbnails/22.jpg)
Reflect:◦Most of the time, interest is
compounded into the
principal more than once a
year.
![Page 23: CHAPTER 3 - migomendoza.weebly.commigomendoza.weebly.com/uploads/5/4/7/4/54745209/compound_interest... · CHAPTER 3 Compound Interest. ... Example 3.1: If P2,000.00 is invested at](https://reader030.vdocument.in/reader030/viewer/2022040211/5e718ae20ecf311a367d6253/html5/thumbnails/23.jpg)
Conversion/Interest Period
◦The time between two
successive conversions
of interest.
![Page 24: CHAPTER 3 - migomendoza.weebly.commigomendoza.weebly.com/uploads/5/4/7/4/54745209/compound_interest... · CHAPTER 3 Compound Interest. ... Example 3.1: If P2,000.00 is invested at](https://reader030.vdocument.in/reader030/viewer/2022040211/5e718ae20ecf311a367d6253/html5/thumbnails/24.jpg)
Conversion:
◦Annually – 1 year
◦Semi-annually – 6 months
◦Quarterly – 3 months
◦Monthly – 1 month
![Page 25: CHAPTER 3 - migomendoza.weebly.commigomendoza.weebly.com/uploads/5/4/7/4/54745209/compound_interest... · CHAPTER 3 Compound Interest. ... Example 3.1: If P2,000.00 is invested at](https://reader030.vdocument.in/reader030/viewer/2022040211/5e718ae20ecf311a367d6253/html5/thumbnails/25.jpg)
Frequency of Conversion
◦The number of conversion
periods at a certain time.
To denote this we will use
minuscule letter m.
![Page 26: CHAPTER 3 - migomendoza.weebly.commigomendoza.weebly.com/uploads/5/4/7/4/54745209/compound_interest... · CHAPTER 3 Compound Interest. ... Example 3.1: If P2,000.00 is invested at](https://reader030.vdocument.in/reader030/viewer/2022040211/5e718ae20ecf311a367d6253/html5/thumbnails/26.jpg)
Frequency of Conversion:
◦Annually – 1
◦Semi-annually – 2
◦Quarterly – 4
◦Monthly – 12
◦Daily – 365/366
![Page 27: CHAPTER 3 - migomendoza.weebly.commigomendoza.weebly.com/uploads/5/4/7/4/54745209/compound_interest... · CHAPTER 3 Compound Interest. ... Example 3.1: If P2,000.00 is invested at](https://reader030.vdocument.in/reader030/viewer/2022040211/5e718ae20ecf311a367d6253/html5/thumbnails/27.jpg)
Nominal Rate
◦The rate of interest in
compound interest. To
denote this we will use the
minuscule letter j.
![Page 28: CHAPTER 3 - migomendoza.weebly.commigomendoza.weebly.com/uploads/5/4/7/4/54745209/compound_interest... · CHAPTER 3 Compound Interest. ... Example 3.1: If P2,000.00 is invested at](https://reader030.vdocument.in/reader030/viewer/2022040211/5e718ae20ecf311a367d6253/html5/thumbnails/28.jpg)
The rate of interest for each conversion period is denoted
by i.◦Formula:
𝑖 =𝑛𝑜𝑚𝑖𝑛𝑎𝑙 𝑟𝑎𝑡𝑒
𝑓𝑟𝑒𝑞𝑢𝑒𝑛𝑐𝑦 𝑜𝑓 𝑐𝑜𝑛𝑣𝑒𝑟𝑠𝑖𝑜𝑛
Equation 3.1
![Page 29: CHAPTER 3 - migomendoza.weebly.commigomendoza.weebly.com/uploads/5/4/7/4/54745209/compound_interest... · CHAPTER 3 Compound Interest. ... Example 3.1: If P2,000.00 is invested at](https://reader030.vdocument.in/reader030/viewer/2022040211/5e718ae20ecf311a367d6253/html5/thumbnails/29.jpg)
The number of conversion periods in the term is denoted
by n.◦Formula:
𝒏 = 𝒕𝒊𝒎𝒆 𝒊𝒏 𝒚𝒆𝒂𝒓𝒔 𝒇𝒓𝒆𝒒𝒖𝒆𝒏𝒄𝒚 𝒐𝒇 𝒄𝒐𝒏𝒗𝒆𝒓𝒔𝒊𝒐𝒏
𝒐𝒓 𝒏 = 𝒕 ∗ 𝒎Equation 3.2
![Page 30: CHAPTER 3 - migomendoza.weebly.commigomendoza.weebly.com/uploads/5/4/7/4/54745209/compound_interest... · CHAPTER 3 Compound Interest. ... Example 3.1: If P2,000.00 is invested at](https://reader030.vdocument.in/reader030/viewer/2022040211/5e718ae20ecf311a367d6253/html5/thumbnails/30.jpg)
Example 3.2
◦If money is invested at
8% compounded
quarterly for 3 years.
![Page 31: CHAPTER 3 - migomendoza.weebly.commigomendoza.weebly.com/uploads/5/4/7/4/54745209/compound_interest... · CHAPTER 3 Compound Interest. ... Example 3.1: If P2,000.00 is invested at](https://reader030.vdocument.in/reader030/viewer/2022040211/5e718ae20ecf311a367d6253/html5/thumbnails/31.jpg)
Formula for Compound Amount:
◦Let:
◦P = the original principal invested
◦i = rate of interest
◦S = compound amount of P
◦n = number of conversion periods
![Page 32: CHAPTER 3 - migomendoza.weebly.commigomendoza.weebly.com/uploads/5/4/7/4/54745209/compound_interest... · CHAPTER 3 Compound Interest. ... Example 3.1: If P2,000.00 is invested at](https://reader030.vdocument.in/reader030/viewer/2022040211/5e718ae20ecf311a367d6253/html5/thumbnails/32.jpg)
Formula for Compound Amount:
◦𝑺 = 𝑷(𝟏 + 𝒊)𝒏
Equation 3.3
![Page 33: CHAPTER 3 - migomendoza.weebly.commigomendoza.weebly.com/uploads/5/4/7/4/54745209/compound_interest... · CHAPTER 3 Compound Interest. ... Example 3.1: If P2,000.00 is invested at](https://reader030.vdocument.in/reader030/viewer/2022040211/5e718ae20ecf311a367d6253/html5/thumbnails/33.jpg)
Where:◦S = compound amount or accumulated value of P at the end
of n periods
◦P = the original principal invested
◦ i = rate of interest = 𝑗
𝑚
j = nominal rate of interest (annual rate)
m = frequency of conversion
◦n = number of conversion periods = 𝑡 ∗ 𝑚
t = term of investment
m = frequency of conversion
![Page 34: CHAPTER 3 - migomendoza.weebly.commigomendoza.weebly.com/uploads/5/4/7/4/54745209/compound_interest... · CHAPTER 3 Compound Interest. ... Example 3.1: If P2,000.00 is invested at](https://reader030.vdocument.in/reader030/viewer/2022040211/5e718ae20ecf311a367d6253/html5/thumbnails/34.jpg)
Accumulation Factor
◦In the compound
amount formula, it is
the factor (1 + 𝑖)𝑛.
![Page 35: CHAPTER 3 - migomendoza.weebly.commigomendoza.weebly.com/uploads/5/4/7/4/54745209/compound_interest... · CHAPTER 3 Compound Interest. ... Example 3.1: If P2,000.00 is invested at](https://reader030.vdocument.in/reader030/viewer/2022040211/5e718ae20ecf311a367d6253/html5/thumbnails/35.jpg)
Example 3.3
◦Find the accumulated value
of P5,000.00 in 4 years if it
is invested at 12%
compounded quarterly.
![Page 36: CHAPTER 3 - migomendoza.weebly.commigomendoza.weebly.com/uploads/5/4/7/4/54745209/compound_interest... · CHAPTER 3 Compound Interest. ... Example 3.1: If P2,000.00 is invested at](https://reader030.vdocument.in/reader030/viewer/2022040211/5e718ae20ecf311a367d6253/html5/thumbnails/36.jpg)
Final Answer:
◦The accumulated
value in 4 years is
P8,023.53.
![Page 37: CHAPTER 3 - migomendoza.weebly.commigomendoza.weebly.com/uploads/5/4/7/4/54745209/compound_interest... · CHAPTER 3 Compound Interest. ... Example 3.1: If P2,000.00 is invested at](https://reader030.vdocument.in/reader030/viewer/2022040211/5e718ae20ecf311a367d6253/html5/thumbnails/37.jpg)
Do you know?
◦The value of (1 + 0.03)16can
be obtained using a scientific
calculator or by the use of
Table II.
![Page 38: CHAPTER 3 - migomendoza.weebly.commigomendoza.weebly.com/uploads/5/4/7/4/54745209/compound_interest... · CHAPTER 3 Compound Interest. ... Example 3.1: If P2,000.00 is invested at](https://reader030.vdocument.in/reader030/viewer/2022040211/5e718ae20ecf311a367d6253/html5/thumbnails/38.jpg)
Example 3.4
◦Find the compound amount
and the compound interest on
P10,000.00 for 9 ¼ years at
6% compounded quarterly.
![Page 39: CHAPTER 3 - migomendoza.weebly.commigomendoza.weebly.com/uploads/5/4/7/4/54745209/compound_interest... · CHAPTER 3 Compound Interest. ... Example 3.1: If P2,000.00 is invested at](https://reader030.vdocument.in/reader030/viewer/2022040211/5e718ae20ecf311a367d6253/html5/thumbnails/39.jpg)
Final Answer:
◦The compound amount
is P17,347.77 and the
compound interest is
P7,347.77.
![Page 40: CHAPTER 3 - migomendoza.weebly.commigomendoza.weebly.com/uploads/5/4/7/4/54745209/compound_interest... · CHAPTER 3 Compound Interest. ... Example 3.1: If P2,000.00 is invested at](https://reader030.vdocument.in/reader030/viewer/2022040211/5e718ae20ecf311a367d6253/html5/thumbnails/40.jpg)
Let’s Practice:◦Find the interest rate (i) for each period, the total
number of conversion periods (n) and the conversion
period (m) at the end of the indicated time. If
principal is P15,000.00, determine also the S and I.
(a) 8 years at 9% compounded semi-annually
(b) 12 years and 6 months at 10% compounded
monthly
![Page 41: CHAPTER 3 - migomendoza.weebly.commigomendoza.weebly.com/uploads/5/4/7/4/54745209/compound_interest... · CHAPTER 3 Compound Interest. ... Example 3.1: If P2,000.00 is invested at](https://reader030.vdocument.in/reader030/viewer/2022040211/5e718ae20ecf311a367d6253/html5/thumbnails/41.jpg)
Assignment:◦Find the interest rate (i) for each period, the total number
of conversion periods (n) and the conversion period (m) at
the end of the indicated time.
(c) 10 years and 9 months at 10.5% compounded quarterly
(d) From April 1, 2015 to December 31, 2007 at 12%
compounded quarterly
(e) From June 1, 2002 to May 31, 2008 at 11%
compounded annually
![Page 42: CHAPTER 3 - migomendoza.weebly.commigomendoza.weebly.com/uploads/5/4/7/4/54745209/compound_interest... · CHAPTER 3 Compound Interest. ... Example 3.1: If P2,000.00 is invested at](https://reader030.vdocument.in/reader030/viewer/2022040211/5e718ae20ecf311a367d6253/html5/thumbnails/42.jpg)
Something to think about…
◦How about when Present
ValueP is missing? What
should we do?
![Page 43: CHAPTER 3 - migomendoza.weebly.commigomendoza.weebly.com/uploads/5/4/7/4/54745209/compound_interest... · CHAPTER 3 Compound Interest. ... Example 3.1: If P2,000.00 is invested at](https://reader030.vdocument.in/reader030/viewer/2022040211/5e718ae20ecf311a367d6253/html5/thumbnails/43.jpg)
LESSON 3.3Finding the Present Value
at Compound Interest
![Page 44: CHAPTER 3 - migomendoza.weebly.commigomendoza.weebly.com/uploads/5/4/7/4/54745209/compound_interest... · CHAPTER 3 Compound Interest. ... Example 3.1: If P2,000.00 is invested at](https://reader030.vdocument.in/reader030/viewer/2022040211/5e718ae20ecf311a367d6253/html5/thumbnails/44.jpg)
Present Value◦It is an amount due in ninterest periods which is
invested at a given rate. We
denote this using majuscule
letter P.
![Page 45: CHAPTER 3 - migomendoza.weebly.commigomendoza.weebly.com/uploads/5/4/7/4/54745209/compound_interest... · CHAPTER 3 Compound Interest. ... Example 3.1: If P2,000.00 is invested at](https://reader030.vdocument.in/reader030/viewer/2022040211/5e718ae20ecf311a367d6253/html5/thumbnails/45.jpg)
Challenge:◦Derive the formula for finding
Present Value P using the
formula for computing for
Compound Amount S.
![Page 46: CHAPTER 3 - migomendoza.weebly.commigomendoza.weebly.com/uploads/5/4/7/4/54745209/compound_interest... · CHAPTER 3 Compound Interest. ... Example 3.1: If P2,000.00 is invested at](https://reader030.vdocument.in/reader030/viewer/2022040211/5e718ae20ecf311a367d6253/html5/thumbnails/46.jpg)
Formula for Present Value P:
◦𝑃 =𝑆
(1+𝑖)𝑛or
◦𝑃 = 𝑆(1 + 𝑖)−𝑛
Equations 3.4 and 3.5
![Page 47: CHAPTER 3 - migomendoza.weebly.commigomendoza.weebly.com/uploads/5/4/7/4/54745209/compound_interest... · CHAPTER 3 Compound Interest. ... Example 3.1: If P2,000.00 is invested at](https://reader030.vdocument.in/reader030/viewer/2022040211/5e718ae20ecf311a367d6253/html5/thumbnails/47.jpg)
Discount Factor◦This refers to the factor
(1 + 𝑖)−𝑛. “To discount an
amount S due in n periods”
means to find its present value
P at n periods before S is due.
![Page 48: CHAPTER 3 - migomendoza.weebly.commigomendoza.weebly.com/uploads/5/4/7/4/54745209/compound_interest... · CHAPTER 3 Compound Interest. ... Example 3.1: If P2,000.00 is invested at](https://reader030.vdocument.in/reader030/viewer/2022040211/5e718ae20ecf311a367d6253/html5/thumbnails/48.jpg)
Example 3.5◦Find the present value of
P18,500.00 due in 5 years if
money is worth 8%
compounded semi-annually.
![Page 49: CHAPTER 3 - migomendoza.weebly.commigomendoza.weebly.com/uploads/5/4/7/4/54745209/compound_interest... · CHAPTER 3 Compound Interest. ... Example 3.1: If P2,000.00 is invested at](https://reader030.vdocument.in/reader030/viewer/2022040211/5e718ae20ecf311a367d6253/html5/thumbnails/49.jpg)
Final Answer:
◦The present value
is P12,497.93.
![Page 50: CHAPTER 3 - migomendoza.weebly.commigomendoza.weebly.com/uploads/5/4/7/4/54745209/compound_interest... · CHAPTER 3 Compound Interest. ... Example 3.1: If P2,000.00 is invested at](https://reader030.vdocument.in/reader030/viewer/2022040211/5e718ae20ecf311a367d6253/html5/thumbnails/50.jpg)
Example 3.6◦A 60 square meter house and lot is
purchased on installment. The buyer
makes a P110,400.00 down-payment
and owes a balance of P257,600.00
payable in 5 years. Find the cash value
of the house and lot if money is worth
10% compounded quarterly.
![Page 51: CHAPTER 3 - migomendoza.weebly.commigomendoza.weebly.com/uploads/5/4/7/4/54745209/compound_interest... · CHAPTER 3 Compound Interest. ... Example 3.1: If P2,000.00 is invested at](https://reader030.vdocument.in/reader030/viewer/2022040211/5e718ae20ecf311a367d6253/html5/thumbnails/51.jpg)
Final Answer:
◦The cash value of
the house and lot is
P157,205.79.
![Page 52: CHAPTER 3 - migomendoza.weebly.commigomendoza.weebly.com/uploads/5/4/7/4/54745209/compound_interest... · CHAPTER 3 Compound Interest. ... Example 3.1: If P2,000.00 is invested at](https://reader030.vdocument.in/reader030/viewer/2022040211/5e718ae20ecf311a367d6253/html5/thumbnails/52.jpg)
Let’s Practice: Solve the following problems:1. Find the present value of P30,700.00 due in 6
years if money is worth 8% compounded quarterly.
2. On the birth of a son, a father wished to invest
sufficient money to accumulate P2,500,000.00 by the
time his son turns 21 years old. If the father invests at
a rate of 10% compounded semi-annually, how much
should the investment be?
![Page 53: CHAPTER 3 - migomendoza.weebly.commigomendoza.weebly.com/uploads/5/4/7/4/54745209/compound_interest... · CHAPTER 3 Compound Interest. ... Example 3.1: If P2,000.00 is invested at](https://reader030.vdocument.in/reader030/viewer/2022040211/5e718ae20ecf311a367d6253/html5/thumbnails/53.jpg)
LESSON 3.6Finding the
Nominal Rate
![Page 54: CHAPTER 3 - migomendoza.weebly.commigomendoza.weebly.com/uploads/5/4/7/4/54745209/compound_interest... · CHAPTER 3 Compound Interest. ... Example 3.1: If P2,000.00 is invested at](https://reader030.vdocument.in/reader030/viewer/2022040211/5e718ae20ecf311a367d6253/html5/thumbnails/54.jpg)
Note:◦The nominal rate
𝒋 can be determined
if 𝑺, 𝑷 and 𝒏 are
given.
![Page 55: CHAPTER 3 - migomendoza.weebly.commigomendoza.weebly.com/uploads/5/4/7/4/54745209/compound_interest... · CHAPTER 3 Compound Interest. ... Example 3.1: If P2,000.00 is invested at](https://reader030.vdocument.in/reader030/viewer/2022040211/5e718ae20ecf311a367d6253/html5/thumbnails/55.jpg)
Example 3.9◦At what nominal rate
compounded semi-annually
will P50,000.00
accumulate to P85,000.00
in 12 years?
![Page 56: CHAPTER 3 - migomendoza.weebly.commigomendoza.weebly.com/uploads/5/4/7/4/54745209/compound_interest... · CHAPTER 3 Compound Interest. ... Example 3.1: If P2,000.00 is invested at](https://reader030.vdocument.in/reader030/viewer/2022040211/5e718ae20ecf311a367d6253/html5/thumbnails/56.jpg)
Final Answer:
◦The nominal
rate is 4.47%
![Page 57: CHAPTER 3 - migomendoza.weebly.commigomendoza.weebly.com/uploads/5/4/7/4/54745209/compound_interest... · CHAPTER 3 Compound Interest. ... Example 3.1: If P2,000.00 is invested at](https://reader030.vdocument.in/reader030/viewer/2022040211/5e718ae20ecf311a367d6253/html5/thumbnails/57.jpg)
Reflect:◦How do you find the
process for finding
nominal rate?
![Page 58: CHAPTER 3 - migomendoza.weebly.commigomendoza.weebly.com/uploads/5/4/7/4/54745209/compound_interest... · CHAPTER 3 Compound Interest. ... Example 3.1: If P2,000.00 is invested at](https://reader030.vdocument.in/reader030/viewer/2022040211/5e718ae20ecf311a367d6253/html5/thumbnails/58.jpg)
◦YAS! I feel
you! It’s very
TEDIOUS!!!!!!
![Page 59: CHAPTER 3 - migomendoza.weebly.commigomendoza.weebly.com/uploads/5/4/7/4/54745209/compound_interest... · CHAPTER 3 Compound Interest. ... Example 3.1: If P2,000.00 is invested at](https://reader030.vdocument.in/reader030/viewer/2022040211/5e718ae20ecf311a367d6253/html5/thumbnails/59.jpg)
Formula:Finding for j:
𝑗 = 𝑖𝑥𝑚
Equation 3.6
![Page 60: CHAPTER 3 - migomendoza.weebly.commigomendoza.weebly.com/uploads/5/4/7/4/54745209/compound_interest... · CHAPTER 3 Compound Interest. ... Example 3.1: If P2,000.00 is invested at](https://reader030.vdocument.in/reader030/viewer/2022040211/5e718ae20ecf311a367d6253/html5/thumbnails/60.jpg)
Formula:
𝑖 =𝑆
𝑃
1𝑛− 1
Equation 3.7
![Page 61: CHAPTER 3 - migomendoza.weebly.commigomendoza.weebly.com/uploads/5/4/7/4/54745209/compound_interest... · CHAPTER 3 Compound Interest. ... Example 3.1: If P2,000.00 is invested at](https://reader030.vdocument.in/reader030/viewer/2022040211/5e718ae20ecf311a367d6253/html5/thumbnails/61.jpg)
Example 3.10◦At what rate compounded
quarterly, will P16,000.00
amount to P20,000.00 in 5
years?
![Page 62: CHAPTER 3 - migomendoza.weebly.commigomendoza.weebly.com/uploads/5/4/7/4/54745209/compound_interest... · CHAPTER 3 Compound Interest. ... Example 3.1: If P2,000.00 is invested at](https://reader030.vdocument.in/reader030/viewer/2022040211/5e718ae20ecf311a367d6253/html5/thumbnails/62.jpg)
Final Answer:
◦The nominal
rate is 4.49%
![Page 63: CHAPTER 3 - migomendoza.weebly.commigomendoza.weebly.com/uploads/5/4/7/4/54745209/compound_interest... · CHAPTER 3 Compound Interest. ... Example 3.1: If P2,000.00 is invested at](https://reader030.vdocument.in/reader030/viewer/2022040211/5e718ae20ecf311a367d6253/html5/thumbnails/63.jpg)
Let’s Practice: Solve the following problems:1. At what nominal rate compounded
semi-annually will P18,000.00
amount to P25,000.00 in 5 years?
2. What rate compounded quarterly will
double any sum of money in 9 years?
![Page 64: CHAPTER 3 - migomendoza.weebly.commigomendoza.weebly.com/uploads/5/4/7/4/54745209/compound_interest... · CHAPTER 3 Compound Interest. ... Example 3.1: If P2,000.00 is invested at](https://reader030.vdocument.in/reader030/viewer/2022040211/5e718ae20ecf311a367d6253/html5/thumbnails/64.jpg)
LESSON 3.7Finding the Time
![Page 65: CHAPTER 3 - migomendoza.weebly.commigomendoza.weebly.com/uploads/5/4/7/4/54745209/compound_interest... · CHAPTER 3 Compound Interest. ... Example 3.1: If P2,000.00 is invested at](https://reader030.vdocument.in/reader030/viewer/2022040211/5e718ae20ecf311a367d6253/html5/thumbnails/65.jpg)
How can we find time?
◦Using Logarithm
◦Interpolation
Method
![Page 66: CHAPTER 3 - migomendoza.weebly.commigomendoza.weebly.com/uploads/5/4/7/4/54745209/compound_interest... · CHAPTER 3 Compound Interest. ... Example 3.1: If P2,000.00 is invested at](https://reader030.vdocument.in/reader030/viewer/2022040211/5e718ae20ecf311a367d6253/html5/thumbnails/66.jpg)
Recall…◦What is your idea
about logarithms?
![Page 67: CHAPTER 3 - migomendoza.weebly.commigomendoza.weebly.com/uploads/5/4/7/4/54745209/compound_interest... · CHAPTER 3 Compound Interest. ... Example 3.1: If P2,000.00 is invested at](https://reader030.vdocument.in/reader030/viewer/2022040211/5e718ae20ecf311a367d6253/html5/thumbnails/67.jpg)
Logarithms◦In mathematics, the logarithm
of a number is the exponent to
which another fixed value, the
base, must be raised to produce
that number.
![Page 68: CHAPTER 3 - migomendoza.weebly.commigomendoza.weebly.com/uploads/5/4/7/4/54745209/compound_interest... · CHAPTER 3 Compound Interest. ... Example 3.1: If P2,000.00 is invested at](https://reader030.vdocument.in/reader030/viewer/2022040211/5e718ae20ecf311a367d6253/html5/thumbnails/68.jpg)
Logarithms◦The idea of logarithms
is to reverse the
operation of
exponentiation.
![Page 69: CHAPTER 3 - migomendoza.weebly.commigomendoza.weebly.com/uploads/5/4/7/4/54745209/compound_interest... · CHAPTER 3 Compound Interest. ... Example 3.1: If P2,000.00 is invested at](https://reader030.vdocument.in/reader030/viewer/2022040211/5e718ae20ecf311a367d6253/html5/thumbnails/69.jpg)
Example 3.11◦How long will it take for
P6,500.00 to become
P9,800.00 if it is invested
at 8% compounded
quarterly?
![Page 70: CHAPTER 3 - migomendoza.weebly.commigomendoza.weebly.com/uploads/5/4/7/4/54745209/compound_interest... · CHAPTER 3 Compound Interest. ... Example 3.1: If P2,000.00 is invested at](https://reader030.vdocument.in/reader030/viewer/2022040211/5e718ae20ecf311a367d6253/html5/thumbnails/70.jpg)
Final Answer:◦It will take 5.18
years for P6,500.00
to become
P9,800.00.
![Page 71: CHAPTER 3 - migomendoza.weebly.commigomendoza.weebly.com/uploads/5/4/7/4/54745209/compound_interest... · CHAPTER 3 Compound Interest. ... Example 3.1: If P2,000.00 is invested at](https://reader030.vdocument.in/reader030/viewer/2022040211/5e718ae20ecf311a367d6253/html5/thumbnails/71.jpg)
Example 3.12◦How long will it take for
P6,000.00 to become
P11,300.00 at 6%
compounded semi-
annually?
![Page 72: CHAPTER 3 - migomendoza.weebly.commigomendoza.weebly.com/uploads/5/4/7/4/54745209/compound_interest... · CHAPTER 3 Compound Interest. ... Example 3.1: If P2,000.00 is invested at](https://reader030.vdocument.in/reader030/viewer/2022040211/5e718ae20ecf311a367d6253/html5/thumbnails/72.jpg)
Final Answer:◦It take 10.71 years
for P6,000.00 to
become P11,300.00.
![Page 73: CHAPTER 3 - migomendoza.weebly.commigomendoza.weebly.com/uploads/5/4/7/4/54745209/compound_interest... · CHAPTER 3 Compound Interest. ... Example 3.1: If P2,000.00 is invested at](https://reader030.vdocument.in/reader030/viewer/2022040211/5e718ae20ecf311a367d6253/html5/thumbnails/73.jpg)
Let’s Practice: Solve the following problems:1. How long will it take for P8,000.00 to
accumulate to P9,500.00 at 8%
compounded semi-annually?
2. After how many years will P21,000.00
accumulate to P42,000.00 if is its
invested at 12% compounded quarterly?
![Page 74: CHAPTER 3 - migomendoza.weebly.commigomendoza.weebly.com/uploads/5/4/7/4/54745209/compound_interest... · CHAPTER 3 Compound Interest. ... Example 3.1: If P2,000.00 is invested at](https://reader030.vdocument.in/reader030/viewer/2022040211/5e718ae20ecf311a367d6253/html5/thumbnails/74.jpg)
JTIYJust to Inform You
![Page 75: CHAPTER 3 - migomendoza.weebly.commigomendoza.weebly.com/uploads/5/4/7/4/54745209/compound_interest... · CHAPTER 3 Compound Interest. ... Example 3.1: If P2,000.00 is invested at](https://reader030.vdocument.in/reader030/viewer/2022040211/5e718ae20ecf311a367d6253/html5/thumbnails/75.jpg)
Something to think about◦What do we usually
do when we
calculate for
nominal rate j?
![Page 76: CHAPTER 3 - migomendoza.weebly.commigomendoza.weebly.com/uploads/5/4/7/4/54745209/compound_interest... · CHAPTER 3 Compound Interest. ... Example 3.1: If P2,000.00 is invested at](https://reader030.vdocument.in/reader030/viewer/2022040211/5e718ae20ecf311a367d6253/html5/thumbnails/76.jpg)
Challenge:◦So we can make
everything else smooth
and easy, can you
derive/think of a direct
formula for nominal rate j?
![Page 77: CHAPTER 3 - migomendoza.weebly.commigomendoza.weebly.com/uploads/5/4/7/4/54745209/compound_interest... · CHAPTER 3 Compound Interest. ... Example 3.1: If P2,000.00 is invested at](https://reader030.vdocument.in/reader030/viewer/2022040211/5e718ae20ecf311a367d6253/html5/thumbnails/77.jpg)
Formula for Nominal Rate:
◦𝑗 = 𝑚𝑆
𝑃
1
𝑛− 1
◦Equation 3.10
![Page 78: CHAPTER 3 - migomendoza.weebly.commigomendoza.weebly.com/uploads/5/4/7/4/54745209/compound_interest... · CHAPTER 3 Compound Interest. ... Example 3.1: If P2,000.00 is invested at](https://reader030.vdocument.in/reader030/viewer/2022040211/5e718ae20ecf311a367d6253/html5/thumbnails/78.jpg)
Derivation of Formula:
◦How to find time
using a formula?
Let’s derive the
formula!
![Page 79: CHAPTER 3 - migomendoza.weebly.commigomendoza.weebly.com/uploads/5/4/7/4/54745209/compound_interest... · CHAPTER 3 Compound Interest. ... Example 3.1: If P2,000.00 is invested at](https://reader030.vdocument.in/reader030/viewer/2022040211/5e718ae20ecf311a367d6253/html5/thumbnails/79.jpg)
Formula for Time:
◦𝑡 =𝑙𝑜𝑔
𝑆
𝑃
𝑚 log(1+𝑖)
◦Equation 3.11
![Page 80: CHAPTER 3 - migomendoza.weebly.commigomendoza.weebly.com/uploads/5/4/7/4/54745209/compound_interest... · CHAPTER 3 Compound Interest. ... Example 3.1: If P2,000.00 is invested at](https://reader030.vdocument.in/reader030/viewer/2022040211/5e718ae20ecf311a367d6253/html5/thumbnails/80.jpg)
Example 3.16:◦When is P47,600.00 due
if its present value of
P38,400.00 is invested at
9% compounded
bimonthly?
![Page 81: CHAPTER 3 - migomendoza.weebly.commigomendoza.weebly.com/uploads/5/4/7/4/54745209/compound_interest... · CHAPTER 3 Compound Interest. ... Example 3.1: If P2,000.00 is invested at](https://reader030.vdocument.in/reader030/viewer/2022040211/5e718ae20ecf311a367d6253/html5/thumbnails/81.jpg)
Bimonthly◦This means every
other month or every
two months. Thus,
m=6.
![Page 82: CHAPTER 3 - migomendoza.weebly.commigomendoza.weebly.com/uploads/5/4/7/4/54745209/compound_interest... · CHAPTER 3 Compound Interest. ... Example 3.1: If P2,000.00 is invested at](https://reader030.vdocument.in/reader030/viewer/2022040211/5e718ae20ecf311a367d6253/html5/thumbnails/82.jpg)
Final Answer
◦The amount will
be due after
2.40 years.