Question

use the formula for computing future value using compound interest to determine the value of an account at the end of 7 years if a principal amount of $2,000 is deposited in an account at an annual interest rate of 5%, and the interest is compounded monthly.

the amount after 7 years will be
(round to the nearest cent as needed.)

Explanation:

Step1: Identify formula and variables

Future value formula: $FV = P(1 + \frac{r}{n})^{nt}$. Here, $P=2000$, $r=0.05$, $n=12$, $t=7$.

Step2: Calculate $\frac{r}{n}$

$\frac{0.05}{12} \approx 0.0041667$

Step3: Calculate $nt$

$12 \times 7 = 84$

Step4: Compute $(1 + 0.0041667)^{84}$

$(1.0041667)^{84} \approx 1.41803$

Step5: Find FV

$2000 \times 1.41803 \approx 2836.06$

Answer:

2836.06