$40,500 are deposited into an account with a 3.8% interest rate, compounded monthly (12 times per year)…

$40,500 are deposited into an account with a 3.8% interest rate, compounded monthly (12 times per year). find the accumulated amount after 20 years. hint: $a = p(1+\frac{r}{k})^{kt}$. round your answer to the nearest cent (hundredth).

$40,500 are deposited into an account with a 3.8% interest rate, compounded monthly (12 times per year). find the accumulated amount after 20 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

$P = 40500$, $r=0.038$, $k = 12$, $t = 20$

Step2: Substitute the values into the compound - interest formula

$A=40500\left(1+\frac{0.038}{12}\right)^{12\times20}$ First, calculate the value inside the parentheses: $\frac{0.038}{12}\approx0.003167$, then $1+\frac{0.038}{12}=1 + 0.003167=1.003167$ Next, calculate the exponent: $12\times20 = 240$ So, $A = 40500\times(1.003167)^{240}$

Step3: Calculate $(1.003167)^{240}$

Using a calculator, $(1.003167)^{240}\approx2.11777$

Step4: Calculate the value of A

$A=40500\times2.11777 = 85779.685$ Rounding to the nearest cent, $A\approx85779.69$

Answer:

$85779.69$