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# Implementing the TVM Concepts

1. (Monthly compounding) If you bought a \$1,000 face value CD that matured in nine months, and which was advertised as paying 9% annual interest, compounded monthly, how much would you receive when you cashed in your CD at maturity?

2. (Annualizing a monthly rate) You credit card statement says that you will be charged 1.05% interest a month on unpaid balances. What is the Effective Annual Rate (EAR) being charged?

3. (FV of annuity due) To finance your newborn daughter's education you deposit \$1,200 a year at the beginning of each of the next 18 years in an account paying 8% annual interest. How much will be in the account at the end of the 18th year?

4. (Rate of return of an annuity) Paul's Perfect Peugeot says they'll sell you a brand new Italian"Iron Man" motor scooter for \$1,699. Financing is available, and the terms are 10% down and payments of \$46.57 a month for 40 months. What annual interest rate is Paul charging you?

5. (Rate of return of an annuity) You would like to have \$1,000,000 40 years from now, but the most you can afford to invest each year is \$1,200. What annual rate of return will you have to earn to reach your goal?

6. (Monthly loan payment) Best Buy has a flat-screen HDTV on sale for \$1,995. If you could borrow that amount from Carl's Credit Union at 12% for 1 year, what would be your monthly loan payments?

7. (Solving for an annuity payment) You would like to have \$1,000,000 accumulated by the time you turn 65, which will be 40 years from now. How much would you have to put away each year to reach your goal, assuming you're starting from zero now and you earn 10% annual interest on your investment?

8. (PV of a perpetuity) If your required rate of return was 12% a year, how much would you pay today for \$100 a month forever? (that is, the stream of \$100 monthly payments goes on forever, continuing to be paid to your heirs after your death)

9. (PV of an uneven cash flow stream) what is the PV of the following project?
(Assume r = 10%)
Year Cash Flow
1 \$10,000
2 \$10,000
3 \$10,000
4 \$20,000

10. (FV of an uneven cash flow stream) what is the FV at the end of year 4 of the following project?
(Assume r = 10%)
Year Cash Flow
1 \$10,000
2 \$10,000
3 \$10,000
4 \$20,000

#### Solution Preview

1. Number of periods=n=9 months
Rate of interest=i= 9%/12=0.75% per month
Face value of CD=PV=\$1000
Amount at maturity=FV=?
FV=PV*(1+i)^n=1000*(1+0.75%)^9=\$1069.56

2. Monthly interest Rate=i=1.05%
Number of compounding=m=12
EAR=(1+i)^m-1=(1+1.05%)^12-1=13.35%

3. Annual deposit=R=\$1200
Number of periods=n=18
Rate of interest=i=8%
It is a case of annuity due.
Future Value of an annuity due is given by
FV=R/i*((1+i)^n-1)*(1+i)=1200/8%*((1+8%)^18-1)*(1+8%)=\$48,535.52

4. Loan amount=PV=price of TV*(1-down payment)=1699*(1-10%)=\$1,529.1
Monthly payment=R=\$46.57
Number of payments=n=40
We know ...

#### Solution Summary

There are 10 problems related to time value of money. Solutions depict the methodology to calculate present value, future value, EAR, annual interest rate, and annuity payments. Detailed working is shown for each of the problems.

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