Question

sid invests $90 in a savings account that earns 2% interest, compounded annually. how much interest will he earn in 6 years? answer in dollars and round to the nearest cent.

Explanation:

Step1: Identify compound amount formula

The formula for compound amount is $A = P(1 + r)^t$, where $P$ is principal, $r$ is annual interest rate, $t$ is time in years.

Step2: Plug in given values

$P = 90$, $r = 0.02$, $t = 6$
$A = 90(1 + 0.02)^6 = 90(1.02)^6$

Step3: Calculate $(1.02)^6$

$(1.02)^6 \approx 1.126162419$

Step4: Compute total amount

$A \approx 90 \times 1.126162419 \approx 101.3546177$

Step5: Find earned interest

Interest = Total amount - Principal
$\text{Interest} \approx 101.3546177 - 90 = 11.3546177$

Step6: Round to nearest cent

Round $11.3546177$ to two decimal places.

Answer:

$11.35$