Leona bought a 1-year, 10,000 certificate of deposit that paid interest at an annual rate of 8 percent compounded...

[BTGmoderatorLU]

Source: Official Guide

Leona bought a 1-year, 10,000 certificate of deposit that paid interest at an annual rate of 8 percent compounded semiannually. What was the total amount of interest paid on this certificate at maturity?

A. $10,464
B. $864
C. $816
D. $800
E. $480

The OA is C

[Scott@TargetTestPrep]

Source: Official Guide

Leona bought a 1-year, 10,000 certificate of deposit that paid interest at an annual rate of 8 percent compounded semiannually. What was the total amount of interest paid on this certificate at maturity?

A. $10,464
B. $864
C. $816
D. $800
E. $480

The OA is C

Solution:

We use the compound interest equation:

Future Value = (Present Value)(1 + r/n)^nt

where r is the annual interest rate (expressed as a decimal), n is the number of compounding periods per year, and t is the amount of time (in years) until maturity.

So we know:

Present Value = 10,000

r = 8% = 0.08

n = 2

t = 1

So we have:

FV = 10,000(1+0.08/2)^(2)(1)

FV = 10,000(1+0.04)^2

FV = 10,000(1.04)(1.04)

FV = 10,000(1.0816) = $10,816

Thus, the amount of interest earned is $10,816 – $10,000 = $816.

Alternate Solution:

We can look at this problem a bit more conceptually. We know that when an investment has a rate of 8% annual interest and it compounds semi-annually (twice a year), the investment earns 4% interest every six months. In this case, we know:

Interest earned for the first six months = 0.04 x $10,000 = $400

Her investment is now worth ($400 + $10,000) = $10,400

Interest earned for the next six months = 0.04 x $10,400 = $416

Thus, the total interest earned = $400 + $416 = $816

Answer: C