GMAT Focus EditionData InsightsMedium
A financial analyst is evaluating the potential returns of two investment strategies, Strategy A and Strategy B, over a 5-year period. Both strategies involve an initial investment of $10,000. The projected annual compound interest rates are: Strategy A: 6% annual compound interest Strategy B: 8% annual compound interest Which strategy will yield a higher total amount after 5 years?
- AStrategy B
- BCannot be determined without knowing the compounding frequency.
- CBoth strategies will yield the same amount.
- DStrategy A
Show answer & explanationAnswer & explanation
Correct answer: A. Strategy B
The formula for compound interest is A = P(1 + r)^t, where A is the final amount, P is the principal, r is the annual interest rate, and t is the number of years. Strategy A: $10,000 * (1 + 0.06)^5 = $10,000 * (1.06)^5 = $10,000 * 1.3382255776 = $13,382.26. Strategy B: $10,000 * (1 + 0.08)^5 = $10,000 * (1.08)^5 = $10,000 * 1.4693280768 = $14,693.28. Strategy B yields a higher total amount.
Why the other options are wrong
- B. The question specifies 'annual compound interest', so frequency is known as annual.
- C. The final amounts are different due to different interest rates.
- D. Strategy A yields $13,382.26.
Compound Interest
Compound interest is the interest on a loan or deposit calculated based on both the initial principal and the accumulated interest from previous periods.
- Interest earns interest.
- Formula: A = P(1 + r/n)^(nt), where n is compounding frequency.
- Increases wealth faster than simple interest over time.
Memory trick: Principal Plus Rate to the Power of Time!