"Leona Bought a 1-Year $10,000 Certificate of Deposit..." — GMAT® Worked Solution

Source: Official Guide for GMAT® Review, 11th Edition

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

Try it before reading on.

Step 1: Eliminate the Impossible Answer

Before doing any math, look at the answer choices and the question. The question asks for the interest paid, not the total value of the account. The principal is $10,000 and the annual rate is 8%. There is no way the interest on $10,000 at 8% for one year exceeds the principal.

(A) is $10,464. That's more than the original investment. If the question asks "how much interest was paid," the answer must be less than the principal. Cross off (A).

About 4% of test takers choose (A), which suggests they computed the total account value instead of the interest. Writing what's asked, every time, prevents this.

Step 2: Split the Annual Rate

"Compounded semiannually" means the interest is calculated twice per year. Split the 8% annual rate into two calculations of 4% each.

The first 4% is calculated on the original principal. The second 4% is calculated on the new principal (original plus the first interest payment). That's what makes compound interest different from simple interest: the second calculation is on a larger amount.

Step 3: Calculate the First Interest Payment

Use fractions rather than decimals to avoid calculation errors, since there's no calculator on the quant section:

$\frac{10{,}000}{1} \times \frac{4}{100}$

Cancel the zeros:

$100 \times 4 = 400$

First interest payment: $400.

New principal for the second half of the year: $10,400 (the original $10,000 plus the $400 interest payment).

Step 4: Calculate the Second Interest Payment

Now calculate 4% on the new principal of $10,400:

$\frac{10{,}400}{1} \times \frac{4}{100}$

Cancel the zeros:

$104 \times 4 = 416$

  104
  x 4
  ---
  416

Second interest payment: $416.

This is $16 more than the first payment, because the second calculation is on the increased principal. That's the advantage of compounding: you earn interest on interest, not just on the original amount.

Step 5: Sum the Interest Payments

The total interest is the sum of both payments:

$400 + 416 = 816$

The answer is (C). The total interest paid at maturity is $816.

Note that this is $16 more than the $800 you would earn with 8% simple annual interest. That $16 difference is the effect of compounding.

Why This Problem Matters

About 19% of test takers miss this problem. The wrong answer distribution tells a clear story about what trips people up:

Choosing (D), $800: about 4% of test takers. This is simple annual interest ($10{,}000 \times 0.08 = 800$), ignoring the compounding entirely. The problem says "compounded semiannually," which means you split the rate and calculate twice. If you see "compounded," simple interest is the wrong approach.

Choosing (B), $864: about 9% of test takers, more than double any other wrong answer. This is the most common mistake: applying 8% twice instead of 4% twice. The calculation would be $10{,}000 \times 0.08 = 800$ for the first period, then $10{,}800 \times 0.08 = 864$ for the second. But that's calculating 8% per period, not 8% annually split into two 4% periods. The annual rate stays 8%; you divide it by the number of compounding periods.

Choosing (A), $10,464: about 4% of test takers. This is the total account value (principal plus interest), not the interest alone. The question asks "what was the total amount of interest paid," not "what was the total value of the certificate." Writing what's asked prevents this.

Choosing (E), $480: rare. This might come from splitting the principal or the rate incorrectly, but the error pattern is less clear.

The two concepts worth flashcarding: "compounded semiannually = split annual rate in half, calculate twice" and "interest paid is not the same as total account value." If you internalize both, this problem type becomes straightforward.

Want the full strategy behind this problem? Read: GMAT® Quant: Three Systems for Algebra, Compound Interest, and Estimation

From Episode 22 of Real GMAT® Problems (The GMAT® Strategy Podcast).

Ready for the next one? "Which of the Following Ratios Is Most Nearly Equal to the Ratio 1 + √5 to 2?..." — GMAT® Worked Solution.