Your local bank offers 4-year certificates of deposit (CD) at a 12 percent annual nominal interest rate compounded quarterly. Determine how much additional interest you will earn over 4 years on a $10,000 CD that is compounded quarterly compared with one that is compounded annually.
A) $6,050
B) $0
C) $310
D) $220

Question

Quizplus · Accepted Answer

For a CD compounded quarterly, the effective annual interest rate is:

(1 + (0.12/4))^4 - 1 = 0.126825 or 12.6825%

For a CD compounded annually, the effective annual interest rate is simply 12%.

After 4 years, the interest earned on a $10,000 CD compounded quarterly is:

$10,000(1 + 0.126825/4)^(4*4) - $10,000 = $17,857.20 - $10,000 = $7,857.20

After 4 years, the interest earned on a $10,000 CD compounded annually is:

$10,000(1 + 0.12)^4 - $10,000 = $16,129.60 - $10,000 = $6,129.60

The additional interest earned on the quarterly compounded CD compared to the annually compounded CD is:

$7,857.20 - $6,129.60 = $1,727.60 or $1,728 rounded to the nearest dollar.

Therefore, the best choice is C, $310, which is not an option. The closest answer is D, $220, but that is incorrect.

Your Local Bank Offers 4-Year Certificates of Deposit (CD) at a 12