Question

1. How much should you deposit today in order to withdraw $5,000 each year for 7 years? Your first withdraw will start 5 year from now and your deposit will earn 4% interest.

2. Which amount is worth more today at 14% interest rate: $1,300 in hand today or $2,500 due in five years?

3. Krystal Magee invested $135,125, 17 months ago. Currently the investment is worth $197,234. Krystal knows that the investment paid interest monthly, but she does not know what yield on her investment. What is Krystal’s annual percentage return (APR) and EAR?

4. A 5 year girl was given a lottery ticket for her recent birthday. The ticket was the grand prize winner and is suppose to pay $80,000 per year after taxes, for 20 years. The state sued, however, and won the case arguing that it would pay the prize as agreed, but it would not begin payment until the girl reaches age of 18 in exactly 13 years. If the appropriate discount rate is 6% annually, what is present value of the girl’s fortune?

5. Suppose you are going to buy a car. The cost of car is $20,000. You have $8,000 for down payment. You can borrow the balance of $12,000 from dealership’s finance company at 2% APR, with monthly payment for 36 months or you can borrow from a bank with 8% APR monthly payment for 3 years, and receive a $2,000 rebate on the purchase price. Assume that if you take the rebate, you will apply it toward the purchase. Which alternative is better deal?

6. You are preparing a vacation to Europe in the future. You plan to save $400 a month beginning today, and estimate you earn 1% per month on your savings. Your goal is to save $6,000. How long it take to save this amount?

7. What is present value of perpetuity of $100 per year if appropriate discount rate is 5%? If discount rate is increased to 15% what is the present value of the perpetuity?

8. Bank of Land lends you money today but requires no payments for 3 years. However, during this interest deferred period the loan accumulated interest at 6% rate, compounded quarterly. The bank amortizes the loan over five year period, requiring quarterly payments and continuing charge 6% annual interest rate, compounded quarterly. What will be the quarterly payment will be on today’s loan of $20,000?

9. Energy Tech company issued an 8% (semiannual payment) 20 year bond 5 years ago. a). If the yield of similar bond today is 6%, what is the bond price? What is the current yield? b). If you expect company to call the bond 3 years from today and will pay the principal plus two years coupon interests as penalty what price you should pay for this bond?

10. Green Co. just paid dividend of $1 per share. The company predicts that the dividend will increase 7% for next 5 years and 5% thereafter forever. If your required rate of return is 6%, what price you should pay for this company's stock?

Answer 1

Question 1

The withdrawals are for 7 years with a constant sum = $5000. therefore it is an annuity. The withdrawals start from the 5th year; i.e. at t=5. We can calculate the Present Value of this annuity considering it as an ordinary annuity. This will provide the Present Value of the annuity at t=4. We can then discount the present value of this annuity by 4 periods to get the amount needed to be deposited today.