Question

a principal of $2400 is invested at 8% interest, compounded annually. how much will the investment be worth after 13 years? use the calculator provided and round your answer to the nearest dollar.

Explanation:

Step1: Recall compound interest formula

The formula for compound interest compounded annually is $A = P(1 + r)^t$, where $A$ is the amount of money accumulated after $n$ years, including interest, $P$ is the principal amount (the initial amount of money), $r$ is the annual interest rate (in decimal form), and $t$ is the time the money is invested for in years.

Step2: Identify the values

Given that $P=\$2400$, $r = 8\%=0.08$, and $t = 13$ years.

Step3: Substitute the values into the formula

Substitute $P = 2400$, $r=0.08$, and $t = 13$ into the formula $A=P(1 + r)^t$. So we have $A=2400\times(1 + 0.08)^{13}$.
First, calculate $(1 + 0.08)^{13}$. $(1.08)^{13}\approx2.719624414$.
Then, multiply this by 2400: $A = 2400\times2.719624414\approx6527.098594$.

Step4: Round to the nearest dollar

Rounding $6527.098594$ to the nearest dollar gives $6527$.

Answer:

$\$6527$