sophia puts $1,000.00 into an account to use for school expenses. the account earns 5% interest, compounded…

sophia puts $1,000.00 into an account to use for school expenses. the account earns 5% interest, compounded quarterly. how much will be in the account after 5 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.

sophia puts $1,000.00 into an account to use for school expenses. the account earns 5% interest, compounded quarterly. how much will be in the account after 5 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 of variables

$P = 1000$, $r=0.05$ (since 5% = 0.05), $n = 4$ (compounded quarterly), $t = 5$.

Step2: Substitute values into formula

$A=1000\left(1+\frac{0.05}{4}\right)^{4\times5}=1000\left(1 + 0.0125\right)^{20}$.

Step3: Calculate the value inside parentheses

$1+0.0125=1.0125$.

Step4: Calculate the exponentiation

$(1.0125)^{20}\approx1.282037$.

Step5: Calculate the final amount

$A = 1000\times1.282037=1282.037\approx1282.04$.

Answer:

$1282.04$