Question

jin invested $96,000 in an account paying an interest rate of 6.9% compounded annually. assuming no deposits or withdrawals are made, how much money, to the nearest hundred dollars, would be in the account after 9 years?

Explanation:

Step1: Recall 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 $r = 6.9\%=0.069$, $P=\$96000$, and $t = 9$ years.

Step3: Substitute the values into the formula

$A=96000\times(1 + 0.069)^9$.
First, calculate $(1 + 0.069)^9$.
$(1+0.069)^9=1.069^9\approx1.82877$.
Then, $A = 96000\times1.82877=175561.92$.

Step4: Round to the nearest hundred dollars

Rounding $175561.92$ to the nearest hundred dollars gives $175600$.

Answer:

$175600$