Question

daniel invested $8,900 in an account paying an interest rate of 3.4% compounded annua assuming no deposits or withdrawals are made, how much money, to the nearest hundred dollars, would be in the account after 8 years?

Explanation:

Step1: Identify compound interest formula

The formula for compound annual interest 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

$r = \frac{3.4\%}{100} = 0.034$

Step3: Plug values into formula

Substitute $P = 8900$, $r = 0.034$, $t = 8$:
$A = 8900(1 + 0.034)^8$

Step4: Calculate the growth factor

First compute $(1.034)^8 \approx 1.3007$

Step5: Compute final amount

$A \approx 8900 \times 1.3007 \approx 11576.23$

Step6: Round to nearest hundred

Round $11576.23$ to the nearest hundred: $11600$

Answer:

$\$11,600$