Question

How long will it take $600 to double if it earns the following rates? Compounding occurs once a year. Round your answers to two decimal places.

1) 5%
2) 15%
3) 21%
4) 100%

Answer 1

To find how long it will take for $600 to double at different interest rates, we can use the formula for compound interest. It will take approximately 13.86 years at a 5% interest rate, 4.77 years at a 15% interest rate, 3.49 years at a 21% interest rate, and 1 year at a 100% interest rate for $600 to double.

Step-by-step explanation:

To find how long it will take for $600 to double, we can use the formula for compound interest. The formula for compound interest is A = P(1 + r/n)^(nt), where A is the final amount, P is the principal (starting amount), r is the annual interest rate (expressed as a decimal), n is the number of times the interest is compounded per year, and t is the number of years. Let's calculate the time it will take for $600 to double at each of the given rates:

1. At 5% interest rate, the formula becomes 1200 = 600(1 + 0.05/1)^(1t). Solving for t gives us t ≈ 13.86 years.
2. At 15% interest rate, the formula becomes 1200 = 600(1 + 0.15/1)^(1t). Solving for t gives us t ≈ 4.77 years.
3. At 21% interest rate, the formula becomes 1200 = 600(1 + 0.21/1)^(1t). Solving for t gives us t ≈ 3.49 years.
4. At 100% interest rate, the formula becomes 1200 = 600(1 + 1/1)^(1t). Solving for t gives us t = 1 year.

Therefore, it will take approximately 13.86 years at a 5% interest rate, 4.77 years at a 15% interest rate, 3.49 years at a 21% interest rate, and 1 year at a 100% interest rate for $600 to double.