$25,300 are deposited into an account with a 4.5% interest rate, compounded monthly (12 times per year)…

$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).

$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).

Answer

Explanation:

Step1: Identify the values

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

Step2: Substitute into the formula

$A=25300\left(1+\frac{0.045}{12}\right)^{12\times25}$ First, calculate the value inside the parentheses: $\frac{0.045}{12}=0.00375$, then $1 + 0.00375=1.00375$. And $12\times25 = 300$. So $A = 25300\times(1.00375)^{300}$.

Step3: Calculate $(1.00375)^{300}$

Using a calculator, $(1.00375)^{300}\approx3.0777$.

Step4: Calculate the final amount

$A=25300\times3.0777 = 77865.81$

Answer:

$77865.81$