Question

You deposit $1,700 at the end of each year into an account paying 9.6 percent interest.

a. How much money will you have in the account in 16 years?
b. How much will you have if you make deposits for 32 years?

Answer 1

To calculate the future value of yearly deposits in an interest-bearing account, the formula FV = P * [(1 + r)^n - 1]/r is used. By applying this formula, students can determine how much money they'll have after 16 and 32 years at a 9.6% interest rate, knowing each annual deposit is $1,700.

Step-by-step explanation:

The student is asking how much money they will have after making yearly deposits into an interest-bearing account for 16 and 32 years at an interest rate of 9.6%.

This calculation involves the future value of an annuity, which is a series of equal payments made at regular intervals. The general formula for the future value of an annuity is FV = P * [(1 + r)^n - 1]/r, where P is the payment amount, r is the interest rate per period, and n is the number of periods.

Convert the annual interest rate to a decimal: 9.6% becomes 0.096.

Calculate the future value of the annuity for 16 years:

Future Value for 16 Years: FV = $1,700 * [(1 + 0.096)^16 - 1] / 0.096

Determine the future value of the annuity for 32 years:

Future Value for 32 Years: FV = $1,700 * [(1 + 0.096)^32 - 1] / 0.096

These calculations will give us the amounts for both scenarios.