University of the West Indies

Department of Management Studies

MS28D Financial Management I

Tutorial #5 - Time Value of Money - Chapter 6

Future Value

1. 6-1

2. Calculate the amount of money that will be in each of the following accounts at the end of the given deposit period:

 Account Amount Deposited Annual Interest Rate Compounded Every..... Months Deposit Period (years) Brown \$ 1,000 10% 12 10 Coles 95,000 12 1 1 Elliott 8,000 12 2 2 Robinson 120,000 8 3 2 Chin 30,000 10 6 4 Daley 15,000 12 4 3

1. At what annual rate would the following have to be invested?

(a) \$500 to grow to \$1,948.00 in 12 years

(b) \$300 to grow to \$422.10 in 7 years

( c) \$50 to grow to \$280.20 in 20 years

1. 6-10

2. How many years will the following take:

(a) \$40 to grow to S88.44 if invested at 12% compounded annually?

(b) \$110 to grow to \$614.79 if invested at 24% compounded annually?

(c)  \$550 to grow to \$1,043.90 if invested at 6% compounded annually?

1. 6-3

2.  What is the value of \$50,000 at the end of three years from today if it earns 20% per annum:

(a) interest paid continuously

(b) interest paid daily

(c)  interest paid each quarter

(d) interest paid semiannually

(e) interest paid every 18 months

1.  If you were to quit UTech at the end of this semester and deposit your next semester’s tuition of \$32,000 in an account paying 20% per annum compounding daily. What effective annual interest rate would you earn? What would be the balance in the account in three years?

2. A local credit card company purports to charge an annual percentage rate of 5.5% per month, a total of 66% per annum. Is this a correct claim? Explain.

3. 6-5

4. You are planning to deposit \$10,000 today in a bank account. Five years from today you expect to withdraw \$7,500. If the account pays 5% interest per year, how much will remain in the account nine years from today?

5. You have just graduated and you plan to work for 8 years and then leave for Canada. You figure you can save \$5,000 a year for 5 years and \$2,500 a year for the last three years. The cash flows will start one year from now. In addition, your grandfather has just given you a \$10,000 graduation gift.

If you put this gift and your future savings in an account paying 10% compounded annually, what will be the amount you will have when you leave for Canada 8 years hence?

1. You would like to start your own retirement plan now by making a deposit of \$25,000 each year in a bank account which will earn 10% interest compounded annually. Your first payment will be made at the end of the year for 20 years at the end of which you will retire. At the end of year 21 you will deposit \$35,000 to the account and then \$45,000, \$60,000 and \$25,000 in the following years (years 22 to 24) representing gratuity payments from your company.

At the end of year 25 when you are ready to begin withdrawing funds from the account what will be its balance?

1. 6-14

2. 6-24

3. 6-26

4. 6-43 (The third line in part C should read "101.60" and not "101.75" )

5. 6-20

Present Value

1. 6-2

2. What is the lump sum you would have to deposit now in order to have the balance at question 13. (above) in the account in 25 years?

3. 6-42

4.  Find the present value of the following cash flow stream, discounted at 5% per annum:

Year 1                        \$1,000
Year 2                        \$4,000
Year3—20                 \$3,000

(a)        assume the cash flows occur at the end of each year

(b)        assume the cash flows occur at the beginning of each year

1. Find the present value of an income stream that has a negative flow of \$100 per year for the first three years, a positive flow of \$200 in the fourth year and a positive flow of \$300 in years five through eight. The appropriate discount rate is 4% for each of the first three years and 5% for each of the later years.

1.  Your father has just inherited a large sum of money and he would like to know how much to save for retirement and how much he can spend now.

For retirement he will deposit a lump sum in an account today (January 1, 2001) and will earn 10% compounded annually. He does not intend to use this money until he retires in 5 years (January 1, 2006), and he assumes he will live for 20 additional years after which he thinks he will die on December 31, 2025.

During his retirement he would like to receive income of \$60,000 per year to be received the first day of each year, with the first payment on January 1, 2006, and the last payment on January 1,2025.

Complicating this objective, however, is his desire to have one final three-year African tour. To finance this he wants to receive \$300,000 on January 1, 2021, (instead of the usual S60,000), and nothing on January 1, 2022, and January 1, 2023, as he will be on tour. In addition, after he dies (January 1, 2026), he wants to leave \$100,000 in his account for you.

How much must he deposit in his account at 10% on January 1, 2001 in order to achieve this goal?

1. 6-25

Perpetuity

1. 6-16

Loan Amortization

1. You borrow \$10,000 at 10% for 5 years. The loan is payable in five equal installments at the beginning of each year.

(a)        What is the annual payment that will completely amortize the loan over 5 years?

(b)        Construct an amortization schedule to show the amount of interest and the amount of principal paid each year.

1. The loan officer of your building society has told you that the interest rate on home loans is 24% per annum for a period of 40 years. Interest is charged monthly on the loan.

(a)        What is the effective annual interest rate on the loan?

(b)        Find the monthly payment on a \$300,000 loan. (assuming that payments are made at month end)

(c)        Prepare an amortization table for the first four months.

(d)        Compute the loan balance just after the end of year 35.

1. 6-19

2. You took a loan from a bank under the following terms: \$150,000 on a reducing balance basis, requiring you to pay \$9,838.07 at the end of each month over the next 24 months.

(a)        What is the monthly interest rate?

(b)        What is the annual nominal interest rate?

(c)        What is the annual effective interest rate?

1. 6-12

2. 6-9

3. 6-45

Comprehensive questions

1. 6-22

2. 6-47

1. Segma Investment Inc. wishes to accumulate funds to provide a retirement annuity for the Vice President of Marketing, Jill Morgan. By contract, Jill will retire exactly 12 years from now. One year after retirement she is entitled to receive an annual payment of \$42,000 for exactly 20 years. If she dies before the end of the 20-year period, the annual payments will pass to her heirs.

During the 12-year “accumulation period,” Segma wishes to fund the retirement annuity by making equal annual end of year deposits into an account earning 9% interest. Once the 20-year “distribution period” begins, Segma plans to move the accumulated monies into an account earning a guaranteed 12% per year.

(a) How large a sum must Segma Investments accumulate by the end of year 12 to provide the 20-year, \$42,000 annuity?

(b) How large must Segma’s equal annual end of year deposits into the account be over the 12-year accumulation period to fully fund Jill’s retirement annuity?

(c) How much would Segma have to deposit annually during the accumulated period if Jill’s retirement annuity was a perpetuity and all other terms were the same as initially described?

1. 6-48