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We are tasked with calculating the annual payment to a sinking fund that will amount to $200,000 after 24 years. The sinking fund pays interest at 5 ¼% (or 5.25%) compounded annually.

This problem uses the sinking fund formula:

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

Where:
- $ A $ is the final amount ($200,000 in this case),
- $ P $ is the annual payment we need to find,
- $ r $ is the annual interest rate (5.25% or 0.0525),
- $ n $ is the number of periods (24 years).

Let's solve for $ P $:

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

I'll calculate this now.The annual payment required for the sinking fund to reach $200,000 after 24 years, with an interest rate of 5.25% compounded annually, is approximately **$4,348.68**.

Would you like more details on how this was calculated or further explanation?

Here are 5 related questions to expand on this topic:
1. What would the annual payment be if the interest rate were higher, say 6%?
2. How would the number of years affect the payment if we wanted to achieve the same $200,000 goal in 20 years instead of 24?
3. How is the sinking fund formula different from regular annuity or loan formulas?
4. What happens to the annual payment if the interest is compounded semi-annually instead of annually?
5. Can you apply this formula to a scenario with monthly payments instead of annual ones?

**Tip**: Always double-check the compounding period (annual, semi-annual, etc.) in interest problems, as it can significantly impact the outcome.

To end with the amount of $200,000 after 24 years, calculate the amount of each annual payment to a sinking fund paying interest at 5 1/4% compounded annually.

Learn how to calculate the annual payment required to reach a sinking fund target of $200,000 after 24 years with 5.25% interest compounded annually. This example demonstrates the use of the sinking fund formula to solve for periodic payments.

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