spencer is saving up money to buy a car. spencer puts $7,000.00 into an account which earns 10% interest…

spencer is saving up money to buy a car. spencer puts $7,000.00 into an account which earns 10% interest, compounded quarterly. how much will he have in the account after 7 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.

spencer is saving up money to buy a car. spencer puts $7,000.00 into an account which earns 10% interest, compounded quarterly. how much will he have in the account after 7 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

$P = 7000$, $r=0.10$ (since 10% = 0.10), $n = 4$ (compounded quarterly), $t = 7$.

Step2: Substitute into the formula

$A=7000\left(1+\frac{0.10}{4}\right)^{4\times7}$. First, calculate the value inside the parentheses: $1+\frac{0.10}{4}=1 + 0.025=1.025$. Then, calculate the exponent: $4\times7 = 28$. So, $A = 7000\times(1.025)^{28}$.

Step3: Calculate $(1.025)^{28}$

Using a calculator, $(1.025)^{28}\approx1.996529$.

Step4: Calculate $A$

$A=7000\times1.996529 = 13975.703$. Rounding to the nearest cent, $A\approx13975.70$.

Answer:

$13975.70$