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 formula for compound interest (compounded annually) is $A = P(1 + r)^t$, where:

• $A$ = final amount
• $P$ = principal amount
• $r$ = annual interest rate (decimal)
• $t$ = time in years

Step2: Convert rate to decimal

$r = \frac{6.9}{100} = 0.069$

Step3: Plug values into formula

Substitute $P = 96000$, $r = 0.069$, $t = 9$:
$A = 96000(1 + 0.069)^9$

Step4: Calculate the growth factor

First compute $1.069^9 \approx 1.873$

Step5: Compute final amount

$A \approx 96000 \times 1.873 = 179808$

Step6: Round to nearest hundred

$179808$ rounded to the nearest hundred is $180000$

Answer:

$\$180000$