Could some one please explian What is a sinking fund payment..
Example at 8% interest compounded quarterly in order to reach $20,000 with in five years the sinking payment would be required at the end of each three month period
A sinking fund payment refers to a periodic amount of money that is set aside and invested over time in order to accumulate a specific target amount by a certain deadline. The purpose of a sinking fund is to ensure that enough money is available in the future to meet a financial obligation or goal.
In your example, the sinking fund payment is required to accumulate $20,000 within five years at an 8% interest rate compounded quarterly. To calculate the sinking fund payment, you need to understand the concept of compound interest.
First, let's convert the annual interest rate to a quarterly interest rate. Since interest is compounded quarterly, divide the annual interest rate by four. Therefore, the quarterly interest rate would be 8%/4 = 2%.
Next, let's calculate the number of compounding periods over the five-year period. Since interest is compounded quarterly, the total number of compounding periods would be 5 years * 4 quarters per year = 20 quarters.
To determine the sinking fund payment, we can use the formula for the future value of an ordinary annuity:
Future Value = Payment * ((1 + r)^n - 1) / r
Where:
- Payment is the sinking fund payment
- r is the quarterly interest rate (2%)
- n is the number of compounding periods (20)
We need to solve for the payment to reach $20,000, so the formula becomes:
$20,000 = Payment * ((1 + 0.02)^20 - 1) / 0.02
To find the sinking fund payment, rearrange the formula:
Payment = $20,000 * 0.02 / ((1 + 0.02)^20 - 1)
Calculating this expression gives you the sinking fund payment required at the end of each three-month period to accumulate $20,000 within five years at an 8% annual interest rate compounded quarterly.