$1,500 are deposited into an account with a 5% interest rate, compounded annually (1 time per year).\nfind…

$1,500 are deposited into an account with a 5% interest rate, compounded annually (1 time per year).\nfind the accumulated amount after 15 years.\nhint: $a = p(1+\frac{r}{k})^{kt}$

$1,500 are deposited into an account with a 5% interest rate, compounded annually (1 time per year).\nfind the accumulated amount after 15 years.\nhint: $a = p(1+\frac{r}{k})^{kt}$

Answer

Explanation:

Step1: Identify the values

$P = 1500$, $r=0.05$, $k = 1$, $t = 15$

Step2: Substitute into the formula

$A=P(1 +\frac{r}{k})^{kt}=1500(1+\frac{0.05}{1})^{1\times15}$

Step3: Calculate the value inside the parentheses

$1+\frac{0.05}{1}=1 + 0.05=1.05$

Step4: Calculate the exponentiation

$(1.05)^{15}\approx2.078928179$

Step5: Multiply by the principal

$A = 1500\times2.078928179\approx3118.39$

Answer:

$3118.39$