lecture 35 yield rates ana nora evans 403 kerchof [email protected] ans5k math 1140 financial...
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Lecture 35Yield Rates
Ana Nora Evans 403 [email protected]://people.virginia.edu/~ans5k
Math 1140 Financial Mathematics
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2Math 1140 - Financial Mathematics
Plan for the rest of the semester
Nov 14, Nov 16, Nov 18 – BondsNov 21, Nov 28 – Introduction to OptionsNov 30, Dec 2, Dec 5 – Project Presentations
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3Math 1140 - Financial Mathematics
A) I like the plan.B) I prefer two classes about bonds and have one
on stocks.C) I want some other topic covered.
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4Math 1140 - Financial Mathematics
Upcoming Deadlines
Nov 18 – HW 12 dueNov 21 – presentation sign-upNov 30 – final report and evaluationsNov 30, Dec 2, Dec 5 – presentations and evaluationsDec 2 – HW 13 (extra credit)
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5Math 1140 - Financial Mathematics
A) I want HW13 to be mandatory.B) I want HW13 to be optional to increase my
homework score.C) I want HW13 to be optional to increase my
extra credit score.D) There should be no HW 13.
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6Math 1140 - Financial Mathematics
Advice
The students that must take the final should start studying for it very seriously.Read the class notes and the textbook starting from the beginning. Come to office hours and ask questions about what is unclear.Solve the homework problems again, without looking at the textbook or solutions.
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7Math 1140 - Financial Mathematics
FinalSimple Interest – sections 1.2, 1.3, 1.4, 1.5, 1.6, 1.7, 1.8, 1.9
Discount Interest – sections 2.1, 2.2, 2.3, 2.4, 2.5
Compound Interest – sections 3.1, 3.2, 3.4, 3.5, 3.6, 3.7
Ordinary Annuities – sections 4.1, 4.2, 4.3, 4.4, 4.5, 4.6
Other Annuities – sections 5.1, 5.2, 5.3, 5.4, 5.5, 5.6
Debt Retirement Methods – sections 6.1, 6.2, 6.3, 6.4, 6.5, 6.6, 6.7
Bonds – handout
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8Math 1140 - Financial Mathematics
Last Time
Comparison of amortization and sinking funds.The sinking fund is more expensive than amortization when the interest rate earned by the fund is smaller than the interest rate paid for the loan. (j<i)
The sinking fund is less expensive than amortization when the interest rate earned by the fund is bigger than the interest rate paid for the loan. (i<j)
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9Math 1140 - Financial Mathematics
Today
Rate of ReturnYield Rates
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10Math 1140 - Financial Mathematics
Rate of Return
The rate of return is the interest rate earned or lost in an investment.The rate of return is calculated by using an equation of value and solving for the interest rate.
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Math 1140 - Financial Mathematics11
Alice buys a note today for $1,000 earning 8% simple interest for 3 years. After 1 year Alice sells the note to Bob who asks for 10% simple interest on his investment.
What is Alice’s rate of return at simple interest?
The maturity value of Alice’s note is:
$1,000(1+0.08×3)
The sell price of the note is:
Simple Interest
20.11
3)0.08$1,000(1
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Math 1140 - Financial Mathematics12
Have:
The amount invested: $1,000.
The amount earned by this investment in 1 year:
Want:
The simple interest rate.
33.033,1$20.11
3)0.08$1,000(1
Pt
PS
Pt
Ii
1000,1$
000,1$33.033,1$
i
%33.3i
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Math 1140 - Financial Mathematics13
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Math 1140 - Financial Mathematics14
Alice buys a note today for $1,000 earning an effective interest rate of 8% for 3 years. After 1 year Alice sells the note to Bob who asks for an effective interest rate of 10% on his investment.
What is Alice’s rate of return?
The maturity value of Alice’s note is:
$1,000(1+0.08)3
The sell price of the note is:
$1,000(1+0.08)3(1+0.1)-2
Compound Interest
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Math 1140 - Financial Mathematics15
Have:
The amount invested: $1,000.
The amount earned by this investment in 1 year:
$1,000(1+0.08)3(1+0.1)-2
Want:
The compound interest rate.
1n
P
Si
%11.4i
1000,1$
0.1)(10.08)$1,000(11
-23
i
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Math 1140 - Financial Mathematics16
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Math 1140 - Financial Mathematics17
Alice loans $10,000 at 7% effective to Carl, to be repaid with 8 annual payments, the first a year from now. Immediately after Carl makes his third payment, Alice sells the right for the remaining payments to Betty at a price to yield 9% effective.
What is Alice’s rate of return?
Step 1: Calculate the annual payment
We use the present value formula of an ordinary annuity.
ni
iPR
)1(1
68.674,1$)07.01(1
000,10$07.08
R
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Math 1140 - Financial Mathematics18
Alice loans $10,000 at 7% effective to Carl, to be repaid with 8 annual payments, the first a year from now. Immediately after Carl makes his third payment, Alice sells the right for the remaining payments to Betty at a price to yield 9% effective.
What is Alice’s rate of return?
Step 2: Calculate the price paid by Betty
We use the present value formula of an ordinary annuity.
i
iRP
n
)1(1
09.0
)09.01(168.674,1$
5P
92.513,6$P
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Math 1140 - Financial Mathematics19
Have:
The amount invested:
PV = $10,000.
3 yearly payments of:
R = $1,674.68
Sell price of the loan:
S = $6,866.92
Want:
The interest rate.
33
)1()1(1
iSi
iRPV
%77.5i
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Math 1140 - Financial Mathematics20
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Math 1140 - Financial Mathematics21
Does this equation look familiar?
A) NPV
B) IRR
C) Ordinary Annuity
D) Never seen something like this before
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22Math 1140 - Financial Mathematics
The yield rate of an investment is the rate of return.The rate of return is the interest rate earned or lost in an investment.The rate of return is calculated by using an equation of value and solving for the interest rate.
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23Math 1140 - Financial Mathematics
Suppose that you have a loan at an effective rate of 6% that requires you to make 12 annual payments of $5000 each. Immediately after making the 5th payment, you contact the lender and ask to repay the loan with 4 more larger payments. The lender agrees, but only if the yield rate on the remaining payments is 7.5% effective. How large are the new payments?
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24Math 1140 - Financial Mathematics
The yield rate (aka interest rate) of the last 4 payments is 7.5%.What is the present value of these payments?A) 12×$5,000B) The outstanding balance after the 5th paymentC) 7×$5,000D) I can’t calculate it
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25Math 1140 - Financial Mathematics
Plan
Step 1: Calculate the outstanding balance after the fifth paymentStep 2: Calculate the new payment
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Math 1140 - Financial Mathematics26
Suppose that you have a loan at an effective rate of 6% that requires you to make 12 annual payments of $5000 each.
Immediately after making the 5th payment, you contact the lender and ask to repay the loan with 4 more larger payments.
The lender agrees, but only if the yield rate on the remaining payments is 7.5% effective.
How large are the new payments?
Step 1: Calculate the outstanding balance after the 5th payment
Which method is the easiest to use?
i
iROB
kn )()1(1
06.0
)06.01(1000,5$
7OB
91.911,27$OB
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Math 1140 - Financial Mathematics27
Suppose that you have a loan at an effective rate of 6% that requires you to make 12 annual payments of $5000 each.
Immediately after making the 5th payment, you contact the lender and ask to repay the loan with 4 more larger payments.
The lender agrees, but only if the yield rate on the remaining payments is 7.5% effective.
How large are the new payments?
Step 2: Calculate the new payment
What do the remaining payments are?
P = $27,911.91
i = 7.5%
n = 7
R = $8,333.59
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Math 1140 - Financial Mathematics28
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29Math 1140 - Financial Mathematics
Suppose that you have a loan at an effective rate of 6% that requires you to make 12 annual payments of $5000 each. Immediately after making the 5th payment, you contact the lender and ask to repay the loan with 4 more larger payments. The lender agrees, but only if the yield rate is 7.5% effective for the entire loan. How large are the new payments?
![Page 30: Lecture 35 Yield Rates Ana Nora Evans 403 Kerchof AnaNEvans@virginia.edu ans5k Math 1140 Financial Mathematics](https://reader036.vdocument.in/reader036/viewer/2022062715/56649d765503460f94a56b04/html5/thumbnails/30.jpg)
Math 1140 - Financial Mathematics30
What changes from the previous problem?
The outstanding value is calculated differently.
We have to use the retrospective method.
First, we calculate the present value of the payments at 6%.
P = $41,919.22
06.0
)06.01(1000,5$
12P
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31Math 1140 - Financial Mathematics
Next, we calculate the outstanding balance using the retrospective method.
i
iRiPOB
kk 1)1()1(
075.0
1)075.01(000,5$)075.01(22.919,41$
55 OB
51.138,31$OB
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32Math 1140 - Financial Mathematics
We calculate the new payment as in the previous exercise:R = $9,296.95
Questions?
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33Math 1140 - Financial Mathematics
Upcoming Deadlines
Friday, Nov 18 – HW 12 dueMonday, Nov 21 – presentation sign-upNov 30 – final report and evaluationsNov 30, Dec 2, Dec 5 – presentations and evaluations