janelle opened a savings account and deposited $2,739.00 as principal. the account earns 15% interest…

janelle opened a savings account and deposited $2,739.00 as principal. the account earns 15% interest, compounded monthly. what is the balance after 9 years? use the formula $a = p(1+\frac{r}{n})^{nt}$, where $a$ is the balance (final amount), $p$ is the principal (starting amount), $r$ is the interest rate expressed as a decimal, $n$ is the number of times per year that the interest is compounded, and $t$ is the time in years. round your answer to the nearest cent.

janelle opened a savings account and deposited $2,739.00 as principal. the account earns 15% interest, compounded monthly. what is the balance after 9 years? use the formula $a = p(1+\frac{r}{n})^{nt}$, where $a$ is the balance (final amount), $p$ is the principal (starting amount), $r$ is the interest rate expressed as a decimal, $n$ is the number of times per year that the interest is compounded, and $t$ is the time in years. round your answer to the nearest cent.

Answer

Explanation:

Step1: Identify the values

$P = 2739$, $r=0.15$, $n = 12$, $t = 9$

Step2: Substitute into formula

$A=2739\left(1+\frac{0.15}{12}\right)^{12\times9}$

Step3: Calculate the exponent part

$12\times9 = 108$ and $\frac{0.15}{12}=0.0125$, so we have $A = 2739(1 + 0.0125)^{108}$

Step4: Calculate the power

$(1 + 0.0125)^{108}\approx3.64727$

Step5: Calculate the final amount

$A=2739\times3.64727\approx9989.87$

Answer:

$9989.87$