Respuesta :
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:
[tex]FV=PV[1+\frac{r}{100}]^{n}[/tex]
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,
[tex]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}[/tex]
The future value is:
[tex]FV=5000[1+0.10]^{14}+3000[1+0.10]^{8}\\=18987.50+6430.77\\=25418.27[/tex]
Thus, the expression to compute the amount in the investment account after 14 years is: FV = [5000 ×(1.10)¹⁴] + [3000 ×(1.10)⁸].
