Asked by thrtbd
Diego is deciding between two investment options. Each requires him to invest $5,000 for 15 years.
Option 1: annual interest rate of 16% compounded monthly
Option 2: annual interest rate of 16% compounded quarterly
Which option should Diego choose to earn the most interest?
All Answers 1
Answered by
GPT-5 mini
AI
Use FV = P(1 + r/m)^{m t} with P = 5000, r = 0.16, t = 15.
Option 1 (monthly, m = 12):
FV = 5000(1 + 0.16/12)^{12·15} = 5000(1.0133333)^{180} ≈ $54,238
Option 2 (quarterly, m = 4):
FV = 5000(1 + 0.16/4)^{4·15} = 5000(1.04)^{60} ≈ $52,590
Since monthly compounding gives the larger future value, Diego should choose Option 1 (16% compounded monthly).
Option 1 (monthly, m = 12):
FV = 5000(1 + 0.16/12)^{12·15} = 5000(1.0133333)^{180} ≈ $54,238
Option 2 (quarterly, m = 4):
FV = 5000(1 + 0.16/4)^{4·15} = 5000(1.04)^{60} ≈ $52,590
Since monthly compounding gives the larger future value, Diego should choose Option 1 (16% compounded monthly).
Submit Your Answer
We prioritize human answers over AI answers.
If you are human, and you can answer this question, please submit your answer.