how much should be invested in annuity earning 12% annual interest, compounded annually to provide a regular income of $45000 for exactly 25 years. (the first payment is to be at the end of the first 12 months)

To determine the amount that needs to be invested in an annuity to provide a regular income of $45,000 for 25 years with a 12% annual interest rate, compounded annually, we can use the formula for the present value of an annuity:

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

Where:
- $ PV $ is the present value (the amount to be invested).
- $ P $ is the payment per period ($45,000).
- $ r $ is the interest rate per period (12% or 0.12).
- $ n $ is the number of periods (25 years).

Let's plug in the values and calculate:

\[
PV = \frac{45000 \times \left(1 - (1 + 0.12)^{-25}\right)}{0.12}
\]

Now, I'll calculate the present value (PV).The amount that should be invested in the annuity to provide a regular income of $45,000 for 25 years, with a 12% annual interest rate compounded annually, is approximately **$352,941.26**.

Would you like more details on this calculation, or do you have any other questions?

Here are 5 related questions:
1. How does the frequency of compounding affect the amount to be invested?
2. What if the interest rate changes? How does it impact the required investment?
3. How much would need to be invested if the payments started immediately rather than at the end of the first year?
4. What is the difference between an ordinary annuity and an annuity due?
5. How would inflation affect the real value of the annuity payments?

**Tip:** Understanding how different interest rates and compounding frequencies impact annuities can help in making more informed investment decisions.

Learn how to calculate the amount to invest in an annuity earning 12% annual interest, compounded annually, to provide a regular income of $45,000 over 25 years. Detailed step-by-step solution using the Present Value of Annuity formula.

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