A teacher is planning to spend $12,500 at the end of every year at the time of his retirement which is planned for 15 years. Assuming a rate of interest of 8% per annum, calculate the amount he has to save to be able to realise his plan.

The teacher wants to spend $12,500 at the end of each year for 15 years after retirement, with an interest rate of 8% per annum. To calculate the amount he needs to save now, we use the **Present Value of an Annuity** formula:

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

Where:
- $ PV $ is the present value (the amount the teacher needs to save now),
- $ P = 12,500 $ (the annual withdrawal),
- $ r = 0.08 $ (the interest rate per period),
- $ n = 15 $ (the number of years of withdrawals).

### Substituting the values into the formula:

\[
PV = 12,500 \times \frac{1 - (1 + 0.08)^{-15}}{0.08}
\]

I'll calculate this now.The teacher needs to save approximately **$106,993.48** at the time of retirement to be able to withdraw $12,500 per year for 15 years, assuming an 8% annual interest rate.

Would you like more details or have any further questions?

Here are 5 related questions:
1. How would the required savings change if the interest rate was lower?
2. What if the teacher wanted to withdraw $15,000 per year instead?
3. How does the length of the withdrawal period affect the required savings?
4. What is the total amount of money the teacher will withdraw over 15 years?
5. How would inflation affect the future value of the $12,500 withdrawals?

**Tip:** The higher the interest rate, the less you need to save initially, as compound interest works in your favor.

Learn how to calculate the amount a teacher needs to save for retirement to withdraw $12,500 annually for 15 years with an 8% interest rate. This problem covers the Present Value of an Annuity formula and the Time Value of Money theorem. Suitable for students and professionals in financial mathematics.

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