"Give me $5,000 today and I'll return $20,000 to you in 5 years," offers the investment broker.To the nearest percent,what annual interest rate is being offered?
A) 25%
B) 29%
C) 32%
D) 60%

Question

Quizplus · Accepted Answer

To calculate the annual interest rate, we can use the formula for compound interest:

A = P(1 + r/n)^(nt)

Where:
A = the future value of the investment ($20,000)
P = the present value of the investment ($5,000)
r = the annual interest rate (what we're trying to find)
n = the number of times the interest is compounded per year (assuming annually in this case)
t = the number of years (5)

Plugging in the values we know, we get:

20,000 = 5,000(1 + r/1)^(1*5)

Simplifying:

4 = (1 + r)^5
4^(1/5) = 1 + r
1.3195 = 1 + r
r = 0.3195 or 31.95%

Rounding to the nearest percent, we get an annual interest rate of 32%, which corresponds to choice C.

"Give Me $5,000 Today and I'll Return $20,000 to You