Question

This question has two parts.

A company will need to have $3,000 four years from now to purchase new equipment. It plans to get this money through four equal investments, with the first investment beginning one year from now.

a. If the company can earn an annual interest of 10%, how much should the company invest per year?

b. In an different scenario, the two changes listed below are to occur today and will continue throughout the next four years. Consider both of these changes simultaneously.

1. The interest rate will increase today and remain at a higher level.

2. There will also be four equal investments, but the first investment will occur immediately.

How will these changes if they occur at the same time affect the answer to the previous part.

Answer 1

Part (a):

The equal investments (assumed to be at yearly intervals) constitute an ordinary annuity with future value (FV) of $3,000 for 4 period

Also given, interest rate= 10%

Amount of each investment= FV/(FVIFA 10%,4) = 3000/4.6410 = $646.41

Part (b)

Increase in interest rate will result in reduction in periodical investments needed since the interest added on each investment during the term will be higher.

Also, if the investments commence immediately, periodical investments needed will be less since the investments fetch interest for one more period, in this case, one more year.

If both these changes take place simultaneously, the periodical investments needed will be less than the amount ascertained in part (a) above.