Beatrice invests $2,000 in an account that pays 5% simple interest.How much more could she have earned over a five-year period if the interest had compounded annually?

Question

Quizplus · Accepted Answer

Using simple interest, the total amount earned over five years would be:

$2,000 x 0.05 x 5 =$500

If the interest had been compounded annually, the formula for the future value would be:

FV = P(1 + r/n)^(n*t)

Where:
P = the principal amount (in this case, $2,000)
r = the annual interest rate (5% or 0.05)
n = the number of times the interest is compounded per year (1 for annual compounding)
t = the number of years (5)

FV = $2,000(1 + 0.05/1)^(1*5) = $2,610.51

The difference between the two amounts is:

$2,610.51 - $2,500 = $110.51

Rounding to the nearest cent, the answer is option D, $52.56.

Beatrice Invests $2,000 in an Account That Pays 5% Simple