If $ 5,000 is invested in an account that earns 8% interest compounded semi-annually, then the interest earned after one

[BTGmoderatorDC]

If $ 5,000 is invested in an account that earns 8% interest compounded semi-annually, then the interest earned after one year would be how much greater than if the $ 5,000 had been invested at 8% simple yearly interest?

A. $ 4
B. $ 8
C. $ 12
D. $ 16
E. $ 432



OA B

Source: Princeton Review

[Scott@TargetTestPrep]

If $ 5,000 is invested in an account that earns 8% interest compounded semi-annually, then the interest earned after one year would be how much greater than if the $ 5,000 had been invested at 8% simple yearly interest?

A. $ 4
B. $ 8
C. $ 12
D. $ 16
E. $ 432



OA B

Solution:

We use the compound interest formula: A = P(1 + r/n)^nt, where P is the original principal of 5,000, r = the annual interest rate of 0.08, n = the number of compounding periods per year, which is 2, and t = the time, in years, which is 1.

The amount in the account after 1 year if the interest is compounded semi-annually is:

A = 5,000 x (1 + 0.08/2)^2 = 5,000 x 1.0816 = $5,408

The amount in the account after 1 year if the interest is simple interest is calculated by using the simple interest formula: A = P + P x r x t, where P is the principal of 5,000, r is the interest rate of 0.08, and t is the time in years, which is 1.

A = 5,000 + 5,000 x 0.08 = 5,000 + 400 = $5,400

So the former is $8 more than the latter.

Answer: B