A financial analyst is evaluating two investment options. Option A offers a 4% annual return compounded quarterly. Option B offers a 4.1% annual return compounded annually. If an initial investment of $10,000 is made for 5 years, which option yields a higher return and by approximately how much?
- AOption B by $43
- BOption A by $25
- COption B by $78
- DOption A by $56
Show answer & explanationAnswer & explanation
Correct answer: A. Option B by $43
Option A: A = P(1 + r/n)^(nt) = 10000(1 + 0.04/4)^(4*5) = 10000(1.01)^20 ≈ 10000 * 1.22019 ≈ $12,201.90. Option B: A = P(1 + r)^t = 10000(1 + 0.041)^5 = 10000(1.041)^5 ≈ 10000 * 1.22238 ≈ $12,223.80. Option B yields $12,223.80 - $12,201.90 = $21.90 more. Closest is $25. (Note: GRE calculator often has more precision, leading to slightly different but consistently ranked results. Using 1.01^20 ≈ 1.22019, 1.041^5 ≈ 1.22238. So difference is ~21.90. Option B by $25 is the closest.) Re-evaluating with more precision yields: Option A: 10000 * (1.01)^20 = 12201.90. Option B: 10000 * (1.041)^5 = 12223.83. Difference = 21.93. Option B by $25 is the closest.
Why the other options are wrong
- B. Option A is not higher. This might be a result of miscalculation or comparing interest earned rather than final amount.
- C. This difference is too large and indicates a calculation error.
- D. Option A is not higher. This is a significant miscalculation.
Compound Interest Comparison
Comparing compound interest involves calculating the future value of an investment under different compounding frequencies and annual interest rates, then finding the difference.
- Compound Interest Formula: A = P(1 + r/n)^(nt).
- A = future value, P = principal, r = annual interest rate (decimal), n = number of times compounded per year, t = time in years.
- Higher compounding frequency (n) generally leads to slightly higher returns for the same nominal rate.
Memory trick: Calculate each option, then find their difference.