Problem Solving

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

If the interest is at an ANNUAL rate of 8 percent compounded semiannually, then EVERY SIX MONTHS, we add 4% interest to the certificate.
No need to apply the compound interest formula. It's just as fast to make the 2 calculations.

After 6 months, the value of the certificate = $10,000 + (4% of $10,000)
= $10,000 + ($400)
= $10,400

After 12 months (aka 1 year), the value of the certificate = $10,400 + (4% of $10,400)
= $10,400 + ($416)
= $10,816

Answer: C

Cheers,
Brent

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