Question

A corporation creates a sinking fund in order to have $730,000 to replace some machinery in 9 years. How much should be placed in this account at the end of each week if the annual interest rate is 8.2% compounded weekly?

Answer 1

To calculate the amount that should be placed in the sinking fund account at the end of each week, we use the formula for compound interest. The principal amount should be approximately $568.73.

Step-by-step explanation:

To calculate the amount that should be placed in the sinking fund account at the end of each week, we need to use the formula for compound interest:

A = P(1 + r/n)^(nt)

Where A is the future value of the investment, P is the principal amount, r is the annual interest rate, n is the number of times interest is compounded per year, and t is the number of years.

In this case, we want to find P, the principal amount. We know that A should be $730,000, r is 8.2% (or 0.082 as a decimal), n is 52 (since interest is compounded weekly), and t is 9 years:

$730,000 = P(1 + 0.082/52)^(52*9)

Simplifying the equation, we have:

$730,000 = P(1.001577)^468

Divide both sides by (1.001577)^468 to isolate P:

P = $730,000 / (1.001577)^468

Using a calculator, we find that P is approximately $568.73. Therefore, approximately $568.73 should be placed in the account at the end of each week.