$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 of P, r, k, and t

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

Step2: Substitute values into the compound - interest formula

$A=P(1 +\frac{r}{k})^{kt}=25300(1+\frac{0.045}{12})^{12\times25}$

Step3: Calculate the value inside the parentheses first

$\frac{0.045}{12}=0.00375$, then $1+\frac{0.045}{12}=1 + 0.00375=1.00375$

Step4: Calculate the exponent

$12\times25 = 300$

Step5: Calculate $(1.00375)^{300}$

Using a calculator, $(1.00375)^{300}\approx3.07728$

Step6: Calculate the final amount A

$A = 25300\times3.07728\approx77855.18$

Answer:

$77855.18$