Suppose you invest $280,000 in an annuity that returns constant annual payments over 9 years, with the first payment one year from now. At an interest rate of 5%, how much is the annual payment you receive?

Equivalent problem structure (as a borrower): Suppose you borrow $280,000 to be paid back in constant annual payments over 9 years with the first payment one year from now. At an interest rate of 5%, how much is the annual payment?

Please round your answer to the nearest hundredth.

To determine the annual payment you would receive (or need to make if borrowing), we can use the formula for the present value of an annuity:

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

Where:
- $ PV $ is the present value of the annuity ($280,000).
- $ P $ is the annual payment (which we need to find).
- $ r $ is the interest rate (5% or 0.05).
- $ n $ is the number of payments (9 years).

We can rearrange the formula to solve for $ P $:

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

Let's calculate the annual payment.The annual payment you would receive (or need to make if borrowing) is **$39,393.22**.

Would you like more details, or do you have any questions?

Here are 5 related questions:
1. How would the annual payment change if the interest rate increased to 6%?
2. What happens to the annual payment if the number of years is extended to 12 years?
3. How does making payments semi-annually instead of annually affect the payment amount?
4. What would the annual payment be if the investment amount was $350,000 instead of $280,000?
5. How does the timing of the first payment (e.g., immediately vs. after 1 year) impact the payment amount?

**Tip:** The concept of time value of money is crucial when calculating annuity payments, as it helps determine how much your investment or loan will grow or cost over time.

Learn how to calculate the annual payment of an annuity when investing $280,000 over 9 years at a 5% interest rate. Understand the concept of present value of annuities and the formula used to determine annual payments. Suitable for advanced high school students and beyond.

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