BTGmoderatorDC wrote: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
OA C
Source: Official Guide
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
