What amount can be paid at the end of every month, in perpetuity, from an endowment of $75,000 earning 8% compounded monthly?
Multiple Choice
$250
$750
$400
$800
$500

To determine the amount that can be paid at the end of every month in perpetuity from an endowment, we use the formula for the payment of a perpetuity.

The formula for the payment $ PMT $ of a perpetuity is:
\[ PMT = PV \times \frac{r}{m} \]

Where:
- $ PV $ is the present value of the endowment ($75,000)
- $ r $ is the annual interest rate (0.08)
- $ m $ is the number of compounding periods per year (12)

Plugging in the values:
\[ PMT = 75,000 \times \frac{0.08}{12} \]

First, calculate the monthly interest rate:
\[ \frac{0.08}{12} = 0.0066667 \]

Now, calculate the payment:
\[ PMT = 75,000 \times 0.0066667 \]
\[ PMT = 500 \]

Therefore, the amount that can be paid at the end of every month in perpetuity from an endowment of $75,000 earning 8% compounded monthly is **$500**.

So, the correct choice is:

**$500**

Would you like further details or explanations on this solution? Here are five more questions you might find interesting:

1. How does changing the interest rate affect the monthly payment in perpetuity?
2. What is the formula for the present value of an ordinary perpetuity?
3. How does the frequency of compounding affect the payments in a perpetuity?
4. How would the payment change if the endowment amount was doubled?
5. What would be the impact on the payment if the interest was compounded quarterly instead of monthly?

**Tip:** Understanding the concept of perpetuity is essential for financial planning, especially for endowments and scholarships, as it ensures a continuous payment stream without depleting the principal.

Learn how to calculate the monthly payment from a $75,000 endowment earning 8% interest compounded monthly. Understand the concept of perpetuity and compound interest formulas. Suitable for advanced high school students and anyone interested in financial planning.

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