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# TVM, Solve for PMT, Annual Percentage Rate, and Add on Interest

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1. Using the simple interest method, find the monthly payments on a \$2,300 installment loan if the funds are borrowed for 18 months at an annual interest rate of 12%. Use financial calculator to answer the question. Round the answer to the nearest cent.

a. \$ ??? per month
b. How much interest will be paid during the first year of this loan? (Use a monthly payment analysis similar to the one in Exhibit 7.6.) Round your intermediate computations and final answers to the nearest cent.
Exhibit 7.6:

2. Jack Colsen wants to buy a new high-end audio system for his car. The system is being sold by two dealers in town, both of whom sell the equipment for the same price of \$2,000. Jack can buy the equipment from Dealer A, with no money down, by making payments of \$118.28 a month for 18 months; he can buy the same equipment from Dealer B by making 36 monthly payments of \$69.33 (again, with no money down). Jack is considering purchasing the system from Dealer B because of the lower payment.

a. Find the APR for Dealer A. Round the answer to 2 decimal places.
b. .Find the APR for Dealer B. Round the answer to 2 decimal places.

3. Patricia Fox plans to borrow \$5,000 and to repay it in 36 monthly installments. This loan is being made at an annual add-on interest rate of 11.5 percent.

a. Calculate the finance charge on this loan, assuming that the only component of the finance charge is interest. Round the answer to the nearest cent.
b. Use your finding in part a. to calculate the monthly payment on the loan. Round the answer to the nearest cent.
c. Using a financial calculator, determine the APR on this loan. Round the answer to 2 decimal places.

#### Solution Summary

The solution uses functions in Excel and calculator to demonstrate how to do this.

\$2.19

## Time Value of Money

Note: Unless otherwise stated, assume that interest is calculated on an annual basis

1) Ian invests \$1000 today in a 3 year CD paying 3.75% annually. He receives the full amount of principal and accrued interest in 3 years. How much will he receive in 2 years?

N i PV PMT FV

2) How much would Sylvia have to invest in a CD today to receive \$1225 in 4 years time if the interest rate payable on the CD is 2.10%

N i PV PMT FV

3) A zero coupon bond is sold at a discount and pays no interest during its life. John invests \$900 in zero coupon bond which promises to pay \$1100 in 5 years time. What is the rate of return on the investment?

N i PV PMT FV

4) Maggie has the opportunity to invest \$1000 in a 5 year CD. She has the option to receive a 4.65% return, compounded quarterly, 4.75% compounded semi-annually, or 4.85% compounded annually. What option will give her the highest total return and how much will she receive in 5 years time?

Quarterly
N i PV PMT FV

Semi-annually
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Annually
N i PV PMT FV

5) Chris invests \$1000 in a 10 year ordinary annuity when prevailing interest rates are 3.5%. How much will he receive annually?

N i PV PMT FV

6) Using the calculator and the Rule of 72s, how long will it take a \$4000 investment to double if the interest rate is 7.3%?

Calculator Method
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Rule of 72s

7a) Helena purchases a condo and obtains a \$250,000 fully amortizing level payment 15 year mortgage bearing an (annual) interest rate of 6.75%. How much will her monthly blended principal and interest payment be?

N i PV PMT FV

7b) For months 1,2 and 3 of the mortgage, determine how much of the total payment is principal and how much is interest and construct an amortization table

Month Beginning
Principal Payment Interest Amortization of Principal Ending Principal
1 250000
2
3

8) Johnson Corp is considering a capex project that will require an investment of \$150,000. It will have a 5 year lifetime and will return the following amounts:

Year 1 \$20,000
Year 2 \$25,000
Year 3 \$80,000
Year 4 \$70,000
Year 5 \$30,000

8a) If at the end of year 5 the project has no salvage value, what is the company's expected annual rate of return (IRR)?

8b) If at the end of year 5 the project has a salvage value of \$20,000, what is the company's expected annual rate of return? [Hint: The salvage value will add to the cash flow that Johnson receives in year 5]

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