Question

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?

Answer 1

Additional Interest  earned in 45 years is $30185.14

Explanation:

Given-

Principal, P = $4500

Rate, r = 7.2%

Time, $t_{1}$ = 40 years

          $t_{2}$= 45 years

Interest = ?

We know,

$A = P ( 1 + \frac{r}{n} )^n^t$

$A = 4500(1 + 0.072)^4^0\\\\A = 4500 * 16.136\\\\A = 72611.25$

To calculate the interest,

$A = P + I\\I = A - P\\\\I = 72611.25 - 4500\\I = 68111.25$

Interest after 45 years:

$A = P ( 1 + \frac{r}{n} )^n^t$

$A = 4500(1 + 0.072)^4^5\\\\A = 4500 * 22.844\\\\A = 102796.39$

Interest-

$A = P + I\\I = A - P\\\\I = 102796.39 - 4500\\I = 98296.39$

Additional Interest  earned in 45 years = $98296.39 - $68111.25

                                                                 = $30185.14

Therefore, additional Interest  earned in 45 years is $30185.14