tucker puts $1,250.00 into an account to use for school expenses. the account earns 10% interest, compounded…

tucker puts $1,250.00 into an account to use for school expenses. the account earns 10% interest, compounded quarterly. how much will be in the account after 8 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.

tucker puts $1,250.00 into an account to use for school expenses. the account earns 10% interest, compounded quarterly. how much will be in the account after 8 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

$P = 1250$, $r=0.10$ (since 10% = 0.10), $n = 4$ (compounded quarterly), $t = 8$

Step2: Substitute into formula

$A=1250\left(1+\frac{0.10}{4}\right)^{4\times8}$ First, calculate the value inside the parentheses: $\frac{0.10}{4}=0.025$, then $1 + 0.025=1.025$. And $4\times8 = 32$. So $A = 1250\times(1.025)^{32}$

Step3: Calculate $(1.025)^{32}$

Using a calculator, $(1.025)^{32}\approx2.20804$.

Step4: Calculate $A$

$A=1250\times2.20804 = 2760.05$

Answer:

$2760.05$