Question

The right expression to calculate how much money will be in an investment account 14 years from now if you deposit $5,000 now and $3,000 six years from now and the account earns a compound interest rate of 10% is ______.

Answer 1

Answer:

The expression to compute the amount in the investment account after 14 years is: FV = [5000 ×(1.10)¹⁴] + [3000 ×(1.10)⁸].

Step-by-step explanation:

The formula to compute the future value is:

$FV=PV[1+\frac{r}{100}]^{n}$

PV = Present value

r = interest rate

n = number of periods.

It is provided that $5,000 were deposited now and $3,000 deposited after 6 years at 10% compound interest. The amount of time the money is invested for is 14 years.

The expression to compute the amount in the investment account after 14 years is,

$FV=5000[1+\frac{10}{100}]^{14}+3000[1+\frac{10}{100}]^{14-6}\\FV=5000[1+0.10]^{14}+3000[1+0.10]^{8}$

The future value is:

$FV=5000[1+0.10]^{14}+3000[1+0.10]^{8}\\=18987.50+6430.77\\=25418.27$

Thus, the expression to compute the amount in the investment account after 14 years is: FV = [5000 ×(1.10)¹⁴] + [3000 ×(1.10)⁸].