Question

1. jackson invests $8,000 at 4.5% interest compounded annually. how much interest will he earn after 3 years? a. $1,080.00 b. $1,129.33 c. $9,080.00 d. $9,129.33

Explanation:

Step1: Recall compound interest formula

The compound interest formula is $A = P(1 + r)^t$, where $A$ is the amount after $t$ years, $P$ is the principal amount, $r$ is the annual interest rate (in decimal), and $t$ is the number of years. First, we need to find the amount $A$ and then subtract the principal $P$ to get the interest earned.

Step2: Convert the interest rate to decimal

The annual interest rate is $4.5\%$, so in decimal form, $r = \frac{4.5}{100} = 0.045$.

Step3: Identify the values of $P$, $r$, and $t$

Here, $P = \$8,000$, $r = 0.045$, and $t = 3$ years.

Step4: Calculate the amount $A$

Substitute the values into the formula: $A = 8000(1 + 0.045)^3$. First, calculate $(1 + 0.045) = 1.045$. Then, $1.045^3 \approx 1.045 \times 1.045 \times 1.045 \approx 1.141166125$. Now, multiply by $8000$: $A \approx 8000 \times 1.141166125 \approx 9129.329$.

Step5: Calculate the interest earned

Interest earned $= A - P$. So, $9129.329 - 8000 \approx 1129.33$.

Answer:

B. $1,129.33$