A company wants to set up a bursary at the university. The bursary should be such that it can forever give an amount of R11297 per year per student to 3 deserving students. If the bursaries are to be awarded at the end of each year (the first bursaries will be given to students exactly one year after the company donates the money to the university), and the university earns interest at a rate of 2.7% per 3-month period, what amount should the company donate to the university? (Give your answer rounded to 2 decimal places. If you think the answer is R1012.3456, type in 1012.35)

To solve this problem, we need to find the present value of a perpetuity that will allow the university to pay out R11297 per year to each of the 3 students, forever.

### Step-by-step approach:

1. **Annual Payout Calculation:**
   The total annual payout will be:
   \[
   \text{Total Annual Payout} = 11297 \times 3 = 33891 \, \text{Rands per year}.
   \]

2. **Interest Rate per Period:**
   The interest rate given is 2.7% per 3-month period. To find the equivalent annual interest rate, we calculate it as follows:
   \[
   r_{\text{annual}} = \left(1 + \frac{2.7}{100}\right)^4 - 1.
   \]
   This formula compounds the 2.7% interest rate four times (since there are 4 quarters in a year).

3. **Perpetuity Formula:**
   The formula for the present value of a perpetuity is:
   \[
   PV = \frac{A}{r_{\text{annual}}}
   \]
   where:
   - \(A\) is the total annual payout (R33891),
   - \(r_{\text{annual}}\) is the annual interest rate as a decimal.

Let's calculate this now.The company should donate **R301,378.54** to the university to support the bursary program that pays R11,297 per year to each of the 3 students, in perpetuity.

Would you like more details on the calculations or have any other questions?

Here are 5 related questions you might be interested in:
1. How does compound interest affect long-term donations?
2. What if the company wanted to support more students with the same bursary?
3. How would the amount change if the interest rate were different?
4. Can we calculate the donation amount for a finite number of years instead of perpetuity?
5. How does the donation amount change if the bursary payout increases annually?

**Tip:** Always check the compounding period when dealing with interest rates, as it impacts the final calculation significantly.

Discover how to calculate the present value of a perpetual bursary that pays R11297 annually to three students, using a quarterly compound interest rate of 2.7%. Learn the perpetuity formula and compounded interest calculation with this step-by-step solution.

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