Find the periodic payment for each sinking fund that is needed to accumulate the given sum under the given conditions. (Round your answer to the nearest cent.)

*FV* = $800,000, *r* = 8.8%, compounded quarterly for 40 years

To find the periodic payment for a sinking fund, we use the formula for the future value of an ordinary annuity. The formula is:

\[
FV = P \times \frac{(1 + r/n)^{nt} - 1}{r/n}
\]

Where:
- $FV$ is the future value of the sinking fund (\$800,000).
- $P$ is the periodic payment (what we want to find).
- $r$ is the annual interest rate (8.8% or 0.088).
- $n$ is the number of compounding periods per year (quarterly compounding means $n = 4$).
- $t$ is the number of years (40 years).

Given values:
- $FV = 800,000$
- $r = 0.088$
- $n = 4$
- $t = 40$

Substitute these into the formula and solve for $P$:

\[
800,000 = P \times \frac{(1 + 0.088/4)^{4 \times 40} - 1}{0.088/4}
\]

Let's break this down step by step to find $P$.The periodic payment for the sinking fund is approximately **$558.39**.

Would you like a detailed explanation or have any questions about this calculation?

Here are 5 related questions for further exploration:
1. How would the periodic payment change if the interest rate were higher?
2. What if the compounding was done monthly instead of quarterly?
3. How does changing the number of years affect the periodic payment?
4. How would the future value be affected if the periodic payments were made monthly instead of quarterly?
5. What is the total amount of payments made over the 40-year period?

**Tip:** The longer the duration and the more frequent the compounding, the lower the periodic payment required to reach the same future value.

Find the periodic payment for each sinking fund that is needed to accumulate the given sum under the given conditions. (Round your answer to the nearest cent.) FV = $800,000, r = 8.8%, compounded quarterly for 40 years.

Discover how to calculate the periodic payment needed for a sinking fund to accumulate $800,000 with an interest rate of 8.8%, compounded quarterly over 40 years. Learn the key concepts of compound interest and future value of annuities, suitable for college-level finance or advanced high school students.

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