Solutions to Time Value of Money Problems

Problem 1: Compute the discounted value of $5000 due in 10 years and 2 months

1. Compute the discounted value of $5000 due in 10 years and 2 months if money is worth 2.75% compounded weekly

2. Determine the future value amount of $400 invested at 6% compounded quarterly for three years and five months.

3. You have the choice of receiving $100 000 now, or  $60 000 now and another $60 000 five years from now. In terms of today—s dollar, which choice is better and by how much? Money is worth 6% compounded annually.

4. In how many days will $580 grow to $600 at 4.5% p.a. compounded monthly?

5. What is the nominal annual rate of interest compounded quarterly at which $420  will accumulate to $1000 in nine years and six months?

6.  What payment is required at the end of each month for five years to repay a loan of $8000 at 8.4% compounded monthly?

7. Aisha contributed $2000 per year for the past 10 years into an RRSP account earning 3.8% compounded annually. Suppose she leaves the accumulated contributions for another five years in the RRSP at the same rate of interest.

a. How much will Aisha have in total in her RRSP account?

b. How much did Aisha contribute?

c. How much interest will have been earned?

8. The municipal building for the City of Lethbridge is considering installation of a system of wind-powered generators. With the system, the city can save $13 000 every six months in expenses. If interest is 4.75% compounded quarterly, how much should the city invest to install the system?

9. Leanna O’Brien receives pension payments of $3200 at the end of every six months from a retirement fund of $50 000. The fund earns 7% compounded semi-annually.

a. How many payments will Seanna receive?

b. What is the size of the final pension payment?

10. When the Littles purchased a home, they borrowed $170 000 as a mortgage to be amortized by making monthly payments for 25 years. Interest is 4.89% compounded semi-annually for a 3-year term.

a. Compute the size of the monthly payment.

b. Determine the balance at the end of the 3-year term.

c. If the mortgage is renewed for a 4-year term at 5.24% compounded semi-annually, what is the size of the monthly payment for the renewal term?

11. A $160 000 mortgage is to be repaid over a 20-year period by monthly payments rounded up to the next-higher $100 increment. Interest is 5.44% compounded semi-annually.

a. Determine the number of rounded payments required to repay the mortgage.

b. Determine the size of the last payment.

c. Calculate the amount of interest saved by rounding the payments up to the next-higher $100 increment

12. A $15 000, 2.5% bond is purchased six years and six months before maturity to yield 3% semi-annually. If the bond interest is payable semi-annually, what is the purchase price of the bond?

13. A company is offered a contract promising annual net returns of $36 000 at the end of each year for seven years. If it accepts the contract, the company must spend $150 000 immediately to expand its plant. After seven years, no further benefits are available from the contract and the plant expansion undertaken will have no residual value. Should the company accept the contract if the required rate of return is 12%