Question

Esther invests in a tax-sheltered annuity, where the money invested, as well as interest earned, is not subject to taxation until withdrawn from the account. Assuming a person invests $2000.00 each year in a tax-sheltered annuity at 10 percent interest compounded annually, let Aₙ​ represent the amount at the end of n years.

How many years will it take for a person to double the initial investment?

Answer 1

Using the Rule of 72, it will take approximately 7.2 years for a $2000 investment at a 10 percent annual interest rate to double.

Step-by-step explanation:

When an individual invests $2000 each year in a tax-sheltered annuity at a 10 percent interest rate compounded annually, the formula to determine the amount of money Aₙ at the end of n years is:
Aₙ = P (1 + r/n)^(nt), where P is the principal amount, r is the annual interest rate, n is the number of times that interest is compounded per year, and t is the time the money is invested in years.

To double the initial investment of $2000, we seek the time t where Aₙ is at least $4000. Using the Rule of 72, which is a simple way to estimate the number of years required to double the investment at a fixed annual rate of interest, we divide 72 by the interest rate:
72 / 10 = 7.2.

Therefore, it will take approximately 7.2 years for the initial investment of $2000 to double at a 10 percent annual interest rate.