Find the amount of each payment to be made into sinking fund so that enough will be present to accumulate the following amount. Payments are made at the end of each period. The interest rate given as per period. $80,000; money earns 4% compounded quarterly for 2 3/4 years

To find the amount of each payment into a sinking fund, we use the **sinking fund formula**:

\[
R = \frac{A \cdot i}{(1 + i)^n - 1}
\]

Where:
- $ R $ is the regular payment,
- $ A $ is the future value (total amount to accumulate),
- $ i $ is the interest rate per period,
- $ n $ is the total number of periods.

Given:
- Future value, $ A = 80,000 $,
- Interest rate = 4% compounded quarterly, so $ i = \frac{0.04}{4} = 0.01 $ per period,
- Time = 2 3/4 years = 2.75 years,
- Number of periods per year = 4 (since it's compounded quarterly).

The total number of periods, $ n $, is:
\[
n = 2.75 \times 4 = 11 \text{ periods}.
\]

Now, substituting the values into the sinking fund formula:

\[
R = \frac{80,000 \cdot 0.01}{(1 + 0.01)^{11} - 1}
\]

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Here are 5 related questions that might be useful:
1. What is the difference between sinking funds and annuities?
2. How does compound interest affect the growth of funds over time?
3. What are the practical applications of sinking funds in financial planning?
4. How do different compounding periods (monthly, quarterly, etc.) influence the future value?
5. How can we calculate the present value of an annuity?

**Tip:** Always ensure the compounding frequency matches the payment frequency when solving financial math problems.

Find the amount of each payment to be made into sinking fund so that enough will be present to accumulate the following amount. Payments are made at the end of each period. The interest rate given as per period. $80,000; money earns 4% compounded quarterly for 2 3/4 years.

Learn how to calculate the periodic payment needed to accumulate $80,000 in a sinking fund with a 4% interest rate compounded quarterly over 2 3/4 years. This guide covers the sinking fund formula, compound interest concepts, and step-by-step calculations. Ideal for high school students and financial math learners.

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