1. Assume that it is now January 1, 2002. On January 1, 2003, you will deposit $1,000 into a savings account that pays 8 percent. a. If t he bank c ompounds inter est annua lly, how much w ill you have in your ac count on January 1, 2006? b. What w ould your Januar y 1, 2006, b alance be if the ba nk used qu arterl y compounding rather than annual compounding? c. Suppose you depo sited t he $1,000 in 4 pa yments of $250 each on January 1 of 2003, 2004, 2005, and 2006. How much would you have in your account on January 1, 2006, based on 8 percent annual compounding? d. Suppose you depo sited 4 equal payments in your account on Janua ry 1 of 2003 , 2004, 2005, and 2006. Assuming an 8 percent interest rate, how large would each of your payments have to be for you to obtain the same ending balance as you calculated in part a 2. An investment pays you $100 at the end of each of the next 3 years. The investment will then pay you $200 at the end of Year 4, $300 at the end of Year 5, and $500 at the end of Year 6. If the interest rate earned on the investment is 8 percent, what is its present value? What is its future value? 3. Which amount is worth more at 14 percent, compounded annually: $1,000 in hand today or $2,000 due in 6 years? 4. While you were a student in college, you borrowed $12,000 in student loans at an interest rate of 9 percent, compounded annually. If you repay $1,500 per year, how long, to the nearest year, will it take you to repay the loan? 5. The prize in last week’s Florida lottery was estimated to be worth $35 million. If you were lucky enough to win, the state will pay you $1.75 million per year over the next 20 years. Assume that the first installment is received immediately. a. If int erest rates are 8 pe rcent, what is the present value o f the pr ize? b. If inte rest rat es are 8 pe rcent, w hat is t he futur e value af ter 20 ye ars? c. How w ould yo ur ans wers c hange if the pay ments were r eceived at the end of each year? 6. Find the future value of the following annuities. The first payment in these annuities is made at the end of Year 1; that is, they are ordinary annuities. Assume that compounding occurs once a year. a. $40 0 per yea r fo r 10 yea rs a t 1 0 per cent. b. $200 per year for 5 years at 5 perc ent. c. $40 0 per y ea r for 5 y ears a t 0 per ce nt. d. Now re work part s a, b, and c assum ing that p ayment s are ma de at the b eginning of each year; that is, they are annuities due. 7. What is the present value of receiving $6,000 seven years from now if the nominal discount rate is 8 percent, discounted continuously?

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7/31/2019 FM Practice

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1. Assume that it is now January 1, 2002. On January 1, 2003, you will deposit $1,000 intoa savings account that pays 8 percent.

a. If the bank compounds interest annually, how much will you have in your accounton January 1, 2006?

b. What would your January 1, 2006, balance be if the bank used quarterly

compounding rather than annual compounding?c. Suppose you deposited the $1,000 in 4 payments of $250 each on January 1 of 2003, 2004, 2005, and 2006. How much would you have in your account onJanuary 1, 2006, based on 8 percent annual compounding?

d. Suppose you deposited 4 equal payments in your account on January 1 of 2003,2004, 2005, and 2006. Assuming an 8 percent interest rate, how large would eachof your payments have to be for you to obtain the same ending balance as youcalculated in part a

2. An investment pays you $100 at the end of each of the next 3 years. The investment willthen pay you $200 at the end of Year 4, $300 at the end of Year 5, and $500 at the end of

Year 6. If the interest rate earned on the investment is 8 percent, what is its present value?What is its future value?

3. Which amount is worth more at 14 percent, compounded annually: $1,000 in hand todayor $2,000 due in 6 years?

4. While you were a student in college, you borrowed $12,000 in student loans at aninterest rate of 9 percent, compounded annually. If you repay $1,500 per year, how long, tothe nearest year, will it take you to repay the loan?

5. The prize in last week’s Florida lottery was estimated to be worth $35 million. If you

were lucky enough to win, the state will pay you $1.75 million per year over the next 20years. Assume that the first installment is received immediately.a. If interest rates are 8 percent, what is the present value of the prize? b. If interest rates are 8 percent, what is the future value after 20 years?c. How would your answers change if the payments were received at the end of each

year?

6. Find the future value of the following annuities. The first payment in these annuities ismade at the end of Year 1; that is, they are ordinary annuities. Assume that compoundingoccurs once a year.

a. $400 per year for 10 years at 10 percent. b. $200 per year for 5 years at 5 percent.c. $400 per year for 5 years at 0 percent.d. Now rework parts a, b, and c assuming that payments are made at the beginning of

each year; that is, they are annuities due.

7. What is the present value of receiving $6,000 seven years from now if the nominaldiscount rate is 8 percent, discounted continuously?