Practice Problems – Chapter 3

1.         Yuppie Yates is establishing a trust fund for his identical twins.   The trust fund will start to make payments to the twins 15 years from today.  They will each receive 10 equal payments of $15,000 per year.  If the fund will earn 8% per year, how much money must Mr. Yates provide today to enable the fund to exactly make these payments? 

2.            Edward Mark will retire 40 years from now, and is planning for his retirement.  He wants to splurge for the first two years of his retirement, and then settle down to a placid existence in Florida.  He wants to accumulate enough savings by the time he retires to have $60,000 to spend for each of the first two years, to buy a $99,000 condo at the end of the second year, and then spend $30,000 each year for the next 20 years.  If he saves equal annual amounts during his 40 year working life, and earns 8% per year on his savings, how much must he save each year to finance his retirement dreams?  (Assume savings occur at the end of each year, and expenses are paid at the beginning of each year.)        

3.         An investment company offers the following savings plan: you invest $100 at the end of each year for 10 years.  In return, you and your descendants receive $100 a year forever, starting at the end of the 11th year.  What rate of return does this savings plan offer?         

4.         Bessie Smith has worked out the following savings plan for the next 15 years.  Her current salary is $50,000, and her salary will increase by 5% each year.  She will save 10% of her salary each year, at the end of each year, for the next 15 years, except that at the end of the fifth year, she will save only 8% of her salary.  If she earns 10% per year on her savings, what is the future value of her savings at the end of 15 years?

5.         Beej Ebbuzz used to be the ruler of the known universe (or at least the world).  When the board of directors decided to oust him from the job, they didn’t want to hurt his feelings too much.  So they made him a low-interest loan as a parting gesture.   They leant him $408 million at an interest rate of 2.3% per year.  The loan is to be repaid in 5 equal installments, with the first payment falling due after one year.  The market interest rate for the loan would have been 4.6% per year.

a) What are the repayments Beej will actually make on the loan?

b) What is the true PV of those repayments?

c) What is the value of this handsome parting gift?

d) Try to come up with a second way to compute the value of the gift.  Verify that you get the same answer as before.

6.         An ordinary annuity pays $2,000 at the end of each quarter for 3 years.  What is the present value of the annuity, if the interest rate is 12% per year compounded quarterly?

7.         An ordinary annuity pays $1,500 every four months for 4 years.  If the interest rate is 15% per year compounded monthly, what is the present value of the annuity today?

8 a)      An ordinary annuity pays $2,500 at the end of each month for 5 years.  What is the present value of the annuity, if the interest rate is 10% per year compounded monthly?

b)   An ordinary annuity pays $800 at the end of each year for 5 years.  What is the present value of the annuity, if the interest rate is 8% per year compounded semi-annually?

9.         An ordinary annuity pays $900 at the end of each month for 5 years.  What is the present value of the annuity, if the discount rate is 9% per year compounded quarterly?

10.         An ordinary annuity will pay $250 each quarter for 6 years.  What is the future value of the annuity  if the interest rate is

a)  9% per year compounded monthly?

b)  9% per year compounded quarterly?

c)  9% per year compounded semi-annually?

d)  9% per year compounded annually?

11.         You are forced to pawn your stereo system to raise emergency cash.  Honest Eddie's offers you $400, and you can redeem your stereo after one and a half months by paying $480.  Vigo Delimit will give you $425 today, redeemable for $481 after one month.  Whose interest rate is lower? 

12.       You want to invest $1,000 for a period of 5 years.  You have a choice between the following interest rates:

Assuming exactly 52 weeks in the year, which rate should you choose?

13.         An eccentric aunt has left you the following legacy in her will.  You will receive a total of 10 payments.  You will get $100 at the end of the first year.  For the first 4 years (time 1 through time 5), your payments will grow by 4% each year.  For the next 5 years, they will grow at 6% each year.  Trying to figure out how she came up with 4% and 6%, you discover that expected inflation is 4% for the first 5 years and 6% for the next 5 years.  The nominal interest rate for the next 10 years is 8%.

a) compute the present value of the legacy using nominal cashflows/discount rates.

b) compute the present value of the legacy using real cashflows/discount rates. 

14.       The usual legal settlement for an industrial accident is the present value of the employee’s lifetime earnings.  A worker has a current salary of $28,000 per year.  He expects to work for 35 years more.  His salary is expected to increase at the rate of 4% a year over this period. 

a) If he is disabled in an industrial accident, what settlement would he receive, if the discount rate is 10% per year, compounded annually?  (Assume he receives a single salary payment at the end of each year)

b) Recalculate the expected settlement amount assuming monthly salary payments.

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