Question
Ted and Alan are in a race to double their money. Ted feels he will win if he puts his $4,000 into a savings account offering 4.5% interest compounded annually. Alan feels he will win because he intends to put his $1,000 into a savings account offering 6% interest compounded annually. Using the rule of 72, StartFraction 72 Over r EndFraction , who will win, and how many years will it take to double his money?
Alan will win. It will take 16 years.
Alan will win. It will take 12 years.
Ted will win. It will take 12 years.
Ted will win. It will take 16 years.
Alan will win. It will take 16 years.
Alan will win. It will take 12 years.
Ted will win. It will take 12 years.
Ted will win. It will take 16 years.
Answers
GPT-4o mini
To determine who will win the race to double their money, we can use the Rule of 72, which states that the number of years it takes to double an investment can be estimated by dividing 72 by the annual interest rate (r%).
For Ted:
- Interest rate = 4.5%
- Years to double = \( \frac{72}{4.5} = 16 \) years
For Alan:
- Interest rate = 6%
- Years to double = \( \frac{72}{6} = 12 \) years
### Conclusion:
- Ted will take 16 years to double his money.
- Alan will take 12 years to double his money.
Therefore, Alan will win, and it will take him 12 years to double his money.
The correct response is:
**Alan will win. It will take 12 years.**
For Ted:
- Interest rate = 4.5%
- Years to double = \( \frac{72}{4.5} = 16 \) years
For Alan:
- Interest rate = 6%
- Years to double = \( \frac{72}{6} = 12 \) years
### Conclusion:
- Ted will take 16 years to double his money.
- Alan will take 12 years to double his money.
Therefore, Alan will win, and it will take him 12 years to double his money.
The correct response is:
**Alan will win. It will take 12 years.**