Question

Find the compound amount and the amount of interest earned by the following deposit. $5100 at 3.2% compounded continuously for 9 years. The future value after 9 years is approximately $ - (Do not round until the final answer. Then round to the nearest cent as needed.)

Answer 1

Answer: The future value after 9 years is $90852.79 .

Compound  interest : $85752.79

Step-by-step explanation:

Formula to find Future value (compounded continuously):-

$F.V.=Pe^{rt}$, where P is the Present Value , r is rate of interest and t is the time period.

Given : Time period : t = 9 years

Present value : P = $5100

Rate of interest =  3.2% = 0.032

Then, $F.V.=5100e^{0.32(9)}$

$F.V.=5100e^{2.88}=5100\times17.8142731796\\\\=90852.793216\approx90852.79$  [Rounded to nearest cents.]

Compound interest : $I= F.V.- P$

$90852.79-5100=85752.79$

Hence, the future value after 9 years is $90852.79