An account paying annual compound interest was opened with $1,000 ten years ago. Today, the account balance is $1,500. If the same interest rate is offered on an account paying simple interest,
How much income would be earned over the same time period?
A) $86.20
B) $92.47
C) $413.80
D) $436.29
E) $500.00

Question

Quizplus · Accepted Answer

Using the compound interest formula, we can find the interest rate:

$1,500 = $1,000(1 + r)^10
1.5 = (1 + r)^10
10log(1.5) = log(1 + r)
r = 0.0471 or 4.71%

Using the simple interest formula, we can find the interest earned:

I = Prt = $1,000(0.0471)(10) = $471

Therefore, the answer is C, $413.80, which is the closest option to $471.

An Account Paying Annual Compound Interest Was Opened with $1,000