Question

Otis has saved $18,500 so far to buy a house. He can put this amount into account that earns 5.1% simple interest, or another with 5.1% compounded annually. Which method of earning interest should he choose simpler compound and how much more interest will the account earn using that method after four years?

F. Compound interest $15,106.30
G. Simple interest $15,106.30
H. Simple interest $298.65
J. Compound interest $298.65

Answer 1

J Compound interest; $298.65

Step-by-step explanation:

Interest compounding pays interest on the interest. For the same annual rate, any amount of compounding will earn more interest.

For short time periods, the effect of compounding is not great. In general, it will be a fraction of the equivalent simple interest rate. Here, the effective multiplier for annual compounding is ...

1.051^4 = 1.22024337

and the effective multiplier for simple interest is ...

1 +0.051·4 = 1.204

Then the difference in interest rate multiplier for the 4-year period is ...

1.22024337 -1.204 = 0.01614337

That fraction of the $18500 principal is $298.65.

Compound interest earns $298.65 more than simple interest in this scenario.

Hope this helps, have an amazing day!