ACT (Enhanced)MathematicsHard
A financial analyst is comparing two investment options. Option 1 offers an annual interest rate of 4% compounded quarterly. Option 2 offers an annual interest rate of 3.8% compounded continuously. If a principal of $10,000 is invested in each option for 5 years, which option yields a higher return and by approximately how much?
- AOption 2 by $108.50
- BOption 1 by $125.00
- COption 1 by $108.50
- DOption 2 by $125.00
Show answer & explanationAnswer & explanation
Correct answer: C. Option 1 by $108.50
To compare the two options, calculate the future value for each using their respective compound interest formulas: A = P(1 + r/n)^(nt) for quarterly compounding and A = Pe^(rt) for continuous compounding. Then, find the difference between the two future values.
Why the other options are wrong
- A. This incorrectly identifies Option 2 as the higher return.
- B. This indicates an error in calculation for one or both options, or the final difference.
- D. This incorrectly identifies Option 2 as the higher return and has an incorrect difference.
Compound Interest Comparison
Evaluating different compounding frequencies (e.g., quarterly vs. continuously) to determine the best investment return.
- Quarterly: A = P(1 + r/n)^(nt)
- Continuously: A = Pe^(rt)
- Higher frequency generally leads to higher returns for the same nominal rate.
Memory trick: Quarterly's 'n', Continuous 'e', then subtract to see.