baldwin opened a savings account and deposited $1,118.00 as principal. the account earns 3% interest…

baldwin opened a savings account and deposited $1,118.00 as principal. the account earns 3% interest, compounded quarterly. what is the balance after 2 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.

baldwin opened a savings account and deposited $1,118.00 as principal. the account earns 3% interest, compounded quarterly. what is the balance after 2 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 values

$P = 1118$, $r=0.03$, $n = 4$, $t = 2$

Step2: Substitute into formula

$A=1118\left(1+\frac{0.03}{4}\right)^{4\times2}$

Step3: Calculate inside parentheses

$1+\frac{0.03}{4}=1 + 0.0075=1.0075$

Step4: Calculate exponent

$4\times2 = 8$

Step5: Calculate power

$1.0075^{8}\approx1.06166778$

Step6: Calculate final amount

$A = 1118\times1.06166778\approx1186.95$

Answer:

$1186.95$