Question

Jim wants to deposit money in an account to save for a new stereo system in two years. He wants to have $4,000 available at the time. The following rates are available to him:
6.2% simple interest
6.1% compounded annually
5.58% compounded semiannually
5.75% compounded quarterly

Which account(s) should he choose if he wants to invest the smallest amount of money now? I was thinking the 5.57% compunded quarterly or 5.58% compounded semiannually

How much money must he invest to accumulate $4,000 in two years'time?

Answer 1

Imagine you start with $1 (or $1,000 if you prefer).

How much would you have at the end of two years, under each of the schemes?

For example, under the second, starting with $1, you would have

$1 * 1.06 = $1.061 at the end of the first year

$1.061 * 1.06 = $1.12466 at the end of the second year

So to end with $4000, you'd have to start with $4000 / 1.12466.

Do the same for the others, and you have your answer.

(And yes, it's one of those two.)