Question

How long will it take $300 to double if it earns the following rates? Compounding occurs once a year. Round your answers to two decimal places.

a. 6%. year(s)
b. 11%. year(s)
c. 17%. year(s)
d. 100%. year(s)

Answer 1

Here's the time it takes for $300 to double at different interest rates:

a. 6%: 12.38 years

b. 11%: 6.56 years

c. 17%: 4.13 years

d. 100%: 1 year (instantaneous doubling)

Option D is answer.

Step-by-step explanation:

We can use the formula for compound interest to find the time for the principal to double:

F = P * (1 + r)^n

where:

F is the final amount (double of the principal)

P is the principal amount ($300)

r is the annual interest rate

n is the number of years

For each interest rate, we rearrange the formula to solve for n:

6%: n = ln(2/3) / ln(1 + 0.06) ≈ 12.38 years

11%: n = ln(2/3) / ln(1 + 0.11) ≈ 6.56 years

17%: n = ln(2/3) / ln(1 + 0.17) ≈ 4.13 years

100%: n = ln(2/3) / ln(1 + 1) = undefined (instantaneous doubling due to infinite rate)

Therefore, depending on the interest rate, it takes between 4.13 and 12.38 years for the initial $300 to double. At 100% interest, the doubling would be immediate.

Option D is answer.