Question

$25,300 are deposited into an account with a 4.5% interest rate, compounded monthly (12 times per year). find the accumulated amount after 25 years. hint: $a = p(1 + \frac{r}{k})^{kt}$ round your answer to the nearest cent (hundredth).

Explanation:

Step1: Identify given values

$P = 25300$, $r = 0.045$, $k = 12$, $t = 25$

Step2: Calculate monthly rate & total periods

$\frac{r}{k} = \frac{0.045}{12} = 0.00375$, $kt = 12 \times 25 = 300$

Step3: Substitute into compound interest formula

$A = 25300 \times (1 + 0.00375)^{300}$

Step4: Compute the accumulated amount

First calculate $(1.00375)^{300} \approx 3.074813$, then $A = 25300 \times 3.074813$

Answer:

$77,792.77$