Calculate the Doubling Time for Different Investment Scenarios

What is the doubling time for the following investments?

a) $5000 invested at 8%, simple interest. (Round to the nearest year.) Doubling Time = [Select ]

b) $5000 invested at 8%, compounded quarterly. (Round to the nearest quarter.) Doubling Time = [Select ]

c) $5000 invested at 8%, compounded continuously. (Round to two decimal places.) Doubling Time = [Select ]

Answer:

The doubling time for the three investments are as follows:

a) $5000 invested at 8%, simple interest: Doubling Time = 9 years.

b) $5000 invested at 8%, compounded quarterly: Doubling Time ≈ 9.01 quarters (rounded to the nearest quarter).

c) $5000 invested at 8%, compounded continuously: Doubling Time ≈ 8.66 years (rounded to two decimal places).

Explanation:

To calculate the doubling time for each investment, we will use the appropriate formula based on the type of interest.

a) Simple Interest:

For simple interest, we use the formula Doubling Time = 72 / r, where r is the interest rate.

Given that $5000 is invested at 8% simple interest, we can calculate the doubling time as follows:

Doubling Time = 72 / 8 = 9 years.

b) Compounded Quarterly:

For compounded interest, we use the formula Doubling Time = ln(2) / (n * ln(1 + r/n)), where n is the number of compounding periods per year.

Given that $5000 is invested at 8% compounded quarterly, we can calculate the doubling time as follows:

Doubling Time = ln(2) / (4 * ln(1 + 0.08/4)) ≈ 9.01 quarters (rounded to the nearest quarter).

c) Compounded Continuously:

For compounded continuously, we use the formula Doubling Time = ln(2) / (r * ln(1 + r)), where r is the interest rate.

Given that $5000 is invested at 8% compounded continuously, we can calculate the doubling time as follows:

Doubling Time = ln(2) / (0.08 * ln(1 + 0.08)) ≈ 8.66 years (rounded to two decimal places).