Question
Suppose you have R1 000 to invest and two of your hostel friends have offered to cut you in on their private money-making schemes. Peter promises to triple you money in 5 years. Warren says he’ll quadruple your money in 7 years. By calculating the interest rate that is compounded annually, for the 2 deals, which is the better deal?
Answers
GPT 3.5
To compare the two deals, we need to calculate the interest rate that is compounded annually for each offer.
For Peter's offer to triple your money in 5 years, we need to solve for the interest rate in the compound interest formula:
Future Value = Present Value * (1 + Interest Rate)^Number of Years
3000 = 1000 * (1 + Interest Rate)^5
3 = (1 + Interest Rate)^5
1.44 = 1 + Interest Rate
Interest Rate = 0.44 or 44%
For Warren's offer to quadruple your money in 7 years, we again need to solve for the interest rate:
4000 = 1000 * (1 + Interest Rate)^7
4 = (1 + Interest Rate)^7
1.52 = 1 + Interest Rate
Interest Rate = 0.52 or 52%
Comparing the two interest rates, Warren's offer of quadrupling your money in 7 years at an interest rate of 52% compounded annually is the better deal compared to Peter's offer of tripling your money in 5 years at an interest rate of 44%.
For Peter's offer to triple your money in 5 years, we need to solve for the interest rate in the compound interest formula:
Future Value = Present Value * (1 + Interest Rate)^Number of Years
3000 = 1000 * (1 + Interest Rate)^5
3 = (1 + Interest Rate)^5
1.44 = 1 + Interest Rate
Interest Rate = 0.44 or 44%
For Warren's offer to quadruple your money in 7 years, we again need to solve for the interest rate:
4000 = 1000 * (1 + Interest Rate)^7
4 = (1 + Interest Rate)^7
1.52 = 1 + Interest Rate
Interest Rate = 0.52 or 52%
Comparing the two interest rates, Warren's offer of quadrupling your money in 7 years at an interest rate of 52% compounded annually is the better deal compared to Peter's offer of tripling your money in 5 years at an interest rate of 44%.