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Mr. Sardinha Math 10
7.1 Simple and Compound Interest
Simple Interest
Simple interest is based on three pieces of information: the principal, the rate, and the time.
Interest: The fee charged for the use of money.
Principal: The money on which interest is paid.
Rate: The percent charged for money borrowed. This is given as a yearly (annual) rate.
Example 1: Find the future amount of an $8000 simple interest investment for 5 years at 6%.
Example 2: A $2100 payment is due in 15 months. Find the principal if the money is borrowed at 11%
simple interest.
Simple Interest and Future Amount
Interest = Principal x Rate x Time
I = P ∙ r ∙ t
Future Amount = Principal + Interest
A = P + I or A = P(1 + r ∙ t)
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Example 3: Yazia borrowed $5200 at 7.5% simple interest to build a swimming pool.
If she paid $2340 interest, find the term of the loan and the monthly payments.
Discount Loans
Sometimes the interest on a loan is paid up front by deducting the amount of the interest the lender
gives you. This type of loan is called a discounted loan.
Example 4: Noushin obtained a 2 year $6000 loan for university. The rate was 8% simple interest and
the loan was a discounted loan.
a) Find the discount.
b) Find the amount of money Noushin received.
c) Find the actual interest rate.
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Compound Interest
When interest is calculated on the principal plus any previously earned interest it is called compound
interest.
To derive a formula for compound interest you need to use the distributive rule, a + ab = a(1 + b),
many times to see a pattern. Remember, the interest for any year is based on principal plus interest of
the year before.
Interest can be compounded more than once a year, such as semi-annually, quarterly, monthly, or daily.
To calculate the interest rate for one compounding period, divide r by the number of compounding
periods per year, n. The number of times interest is compounded in t years is n ∙ t.
For compound interest questions, below are typical scenarios for n:
interest calculated monthly: n = interested calculated bi-monthly n =
interest calculated quarterly: n = interest calculated daily: n =
interest calculated annually: n = interest calculated semi-anually: n =
interest calculated weekly: n = interest calculated bi-weekly: n =
Compound Interest Formula
𝐴 = 𝑃 (1 +𝑟
𝑛)𝑛𝑡
where: A = the final amount, P = principal, or initial amount, r = rate of yearly interest,
n = number of times yearly interest is compounded per year, t = time in years
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Example 5: Suppose that $8000 is invested for 3 years at 6%.
a) Find the amount of simple interest paid.
b) Find the compound interest, if interest in calculated annually.
Example 6: To have savings for university, the parents of a child invest $25 000 in a savings plan
paying 6% interest compounded quarterly. How much money will they have in 18 years?
Example 7: How much would you have to invest into a 10 year bond paying 4.2% compounded
weekly to make it worth $5000 at the end of its term?
Mickelson Workbook: pp.281–283 #1 – 4 (all), 5 – 12 (any six questions)