Question

At the beginning of year 1, Mike invests $800 at an annual compound interest rate of 3%. He makes no deposits to or withdrawals from the account. Which example explicit formula can be used to find the account's balance at the beginning of year 7.

Answer 1

C. A(7) = 800·(1 +0.03)^(7-1)

Explanation:

Note that the times are described as "the beginning of year 1" and "the beginning of year 7." If you consider the formula to be the one marked (choice D), you find the general case is ...

A(n) = 800·1.03^n

When you put in 1 for n, you see it gives you ...

A(1) = 800·1.03^1 = 824 . . . . . . . incorrect value for "the beginning of year 1"

The exponent of 1.03 needs to be the difference in year numbers: 7-1, as in choice C.

The appropriate formula is ...

A(7) = 800·(1 +0.03)^(7-1)