Question

1. Calculate the annual payment that must be made if you would like to save up $50,000 by t=8. Assume you are making these payments at the beginning of the year. Assume the interest rate to be 3.8% per annum.

2. Calculate the present value of an annuity due which pays 500 every year for the next five years, if the interest rate is 5%.

3. You recently got promoted at your job. You have since decided to buy your dream car which costs $97,000. The car dealer tells you to pay 11,000 at the end of every year for the next 7 years after which you can take possession of the car at t=7. Given a market interest rate of 13%, is this a good deal?

**Please show answer solutions using financial calculator**

Answer 1

1. Let the annual payment be A. So, writing the future value equation:

50000 = A x (1.038^8 + 1.038^7 + ... + 1.038)

A = 5265.109

2. The present value equation will look like:

PV = 500 + 500/1.05 + 500/1.05^2 + 500/1.05^3 + 500/1.05^4 = $2272.975

3. If we use the market interest rate, the present value of the payments will become:

PV = 11000/1.13 + 11000/1.13^2 + ... + 11000/1.13^7 = 48648.71.

Hence, we see that going by the market interest rates, the present value should be only about 48648.71 therefore, it is more prudent to go by the installment payments. Hence, this is a good deal.