# What am I doing wrong in this math problem?

Soandso has \$3,043 in her savings account. If she leaves it there for 15 years at a rate of 2.5%, compounded anually, what will the interest be?

So I set it up in the compound interest formula . . . “plug and chug” as my old stats professor used to say:

P(1 + r/n)^nt

=

3043(1 + 0.025/15)^225

=

\$4,426.16

-\$3,043

= \$1,383.16

Why are you dividing the 2.5% by 15? It’s already an annual rate and you’re compounding annually. That’s one mistake. The other mistake is your exponent. The exponent is the number of compound periods, which is 15. Finally, what you are computing with your formula is not the interest; it’s the future value amount. You have to subtract off the original principal.

The mistake you’re making is that the value of n is 1, not 15:

P = principal = \$3,043

r = annual interest rate = 0.025

n = number of times compounded per year = 1

t = number of years = 15

3043 * (1 + 0.025 / 1) ^ (1 * 15) = 4407.17

4407.17 - 3043 = 1364.17

:smack::smack::smack::smack::smack:

It’s weird how I got so close with such a huge mistake. Twenty bucks over 15 years.

Thank you.

not really.

the number of times you compound would not make much difference at such a low interest rate. Even with continuous compounding your accumulated amount would be \$4427.54 making \$1384.54 in interest.

Think about it this way. At 0% interest, the number of times you compound a year would have no difference on the final amount.