Question

josue invested $160 in an account paying an interest rate of 1.8% compounded annually. assuming no deposits or withdrawals are made, how much money, to the nearest dollar, would be in the account after 5 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

The annual interest rate $r = 1.8\%=0.018$. The principal amount $P=\$160$ and the number of years $t = 5$.

Step3: Substitute values into the formula

$A=160\times(1 + 0.018)^5$.
First, calculate $(1 + 0.018)^5$.
$(1 + 0.018)^5=1.018^5$.
$1.018^5=1.018\times1.018\times1.018\times1.018\times1.018\approx1.093299$.
Then, $A = 160\times1.093299\approx175$.

Answer:

$175$