Question

skylar invested $90,000 in an account paying an interest rate of 5% compounded annually. assuming no deposits or withdrawals are made, how much money, to the nearest cent, would be in the account after 13 years?

Explanation:

Step1: Identify compound - interest formula

The compound - interest formula is $A = P(1 + r)^t$, where $A$ is the amount of money in the account after $t$ years, $P$ is the principal amount (initial investment), $r$ is the annual interest rate (in decimal form), and $t$ is the number of years.

Step2: Convert the interest rate to decimal

Given $r = 5\%=0.05$, $P=\$90000$, and $t = 13$ years.

Step3: Substitute values into the formula

$A=90000\times(1 + 0.05)^{13}$.
First, calculate $(1 + 0.05)^{13}$. Using a calculator, $(1.05)^{13}\approx1.885649$.
Then, $A = 90000\times1.885649$.
$A\approx169708.41$.

Answer:

$169708.41$