Question

Use the compound interest formula to compute the total amount accumulated and the interest earned. $4000 for 3 years at 7% compounded semiannually. The amount in the account is $ 4917.02. (Do not round until the final answer. Then round to the nearest cent as needed.) The interest earned is $( (Do not round until the final answer. Then round to the nearest cent as needed.)

Answer 1

To compute the total amount accumulated and the interest earned using the compound interest formula, we can use the following formula:

A = P(1 + r/n)^(nt)

Where:
A = Total amount accumulated
P = Principal amount (initial investment)
r = Annual interest rate (as a decimal)
n = Number of times interest is compounded per year
t = Number of years

Given:
P = $4000
r = 7% = 0.07 (as a decimal)
n = 2 (compounded semiannually, i.e., twice per year)
t = 3 years
A = $4917.02

We can now solve for the interest earned:

4917.02 = 4000(1 + 0.07/2)^(2*3)

4917.02/4000 = (1 + 0.035)^6

1.2292555 = (1 + 0.035)^6

Taking the 6th root of both sides:

(1.2292555)^(1/6) = 1 + 0.035

1.035 = 1.035

So the interest rate is 3.5%.

To calculate the interest earned, we subtract the principal amount from the total amount accumulated:

Interest earned = Total amount accumulated - Principal amount
Interest earned = $4917.02 - $4000
Interest earned = $917.02

Therefore, the interest earned is $917.02.