You are depositing $4,500 today at an annual interest rate of 7.2 percent. How much additional interest will you earn if you leave the money invested for 45 years instead of 40 years?
A) $25,723.08
B) $30,185.14
C) $22,441.56
D) $6,370.69
E) $11,590.93

Question

Quizplus · Accepted Answer

Using the formula for compound interest, we have:

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

where:

A = final amount
P = initial deposit
r = annual interest rate (as a decimal)
n = number of times the interest is compounded per year
t = number of years

If we assume the interest is compounded annually (n = 1), we can find the final amount after 40 years:

A1 = 4500(1 + 0.072/1)^(1*40) = $51,880.88

Similarly, we can find the final amount after 45 years:

A2 = 4500(1 + 0.072/1)^(1*45) = $82,066.02

The difference in interest earned is:

A2 - A1 = $82,066.02 - $51,880.88 = $30,185.14

Therefore, the additional interest earned by leaving the money invested for 45 years instead of 40 years is $30,185.14.

The correct answer is B.

You Are Depositing $4,500 Today at an Annual Interest Rate