Question

A corporation creates a sinking fund in order to have $520,000 to replace some machinery in 10 years. How much should be placed in this account at the end of each quarter if the annual interest rate is 4.2% compounded quarterly? (Round your answers to the nearest cent.) How much interest would they earn over the life of the account? $

Answer 1

To find the amount that should be placed in the sinking fund at the end of each quarter, use the formula for the future value of an ordinary annuity. After performing the calculations, the amount that should be placed in the sinking fund at the end of each quarter is approximately $4,368.45.

Step-by-step explanation:

To find the amount that should be placed in the sinking fund at the end of each quarter, we can use the formula for the future value of an ordinary annuity:

Future Value = P * ((1 + r/n)^(nt) - 1) / (r/n)

In this case, P represents the periodic payment, r represents the annual interest rate, n represents the number of compounding periods per year, and t represents the number of years.

Given that the future value is $520,000, the annual interest rate is 4.2% compounded quarterly, and the time period is 10 years, we can plug these values into the formula:

P = 520,000 * (0.0425/4) * (1 + 0.0425/4)^(4*10) / ((1 + 0.0425/4)^(4*10) - 1)

After performing the calculations, the amount that should be placed in the sinking fund at the end of each quarter is approximately $4,368.45.