A company wants to set up a bursary at the university. The bursary should be such that it can forever give R6128 per year per student to 4 deserving students. If the bursaries are to be awarded at the beginning of each year (the first bursaries must be given to the students on the day that the company gives the university the donation) and the university earns interest at a rate of 1.4% per 2-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)

The situation described involves a **perpetual bursary** that pays out a fixed amount every year. The company wants to give R6128 per year to 4 students, meaning the total annual payout will be:

\[
4 \times R6128 = R24512
\]

The interest is compounded every 2 months at a rate of **1.4%** per period. To solve this, we'll break it down step by step:

### Step 1: Convert the interest rate to an annual rate.
There are 6 two-month periods in a year. The effective annual interest rate \( i_{yearly} \) can be found using the formula for compound interest:

\[
i_{yearly} = (1 + 0.014)^6 - 1
\]

### Step 2: Calculate the donation required.
The bursary must be perpetual, meaning it will continue forever. This implies that the donation should be the present value of a **perpetuity**, which pays out \( R24512 \) annually. The formula for the present value \( PV \) of a perpetuity is:

\[
PV = \frac{\text{annual payment}}{\text{annual interest rate}}
\]

Now let's calculate these values.The company should donate **R281,761.83** to the university in order to fund the bursary that pays R6128 per year to 4 students indefinitely.

Do you have any questions or would you like further details on the calculations?

Here are 5 related questions you might explore:
1. How would the donation amount change if the interest rate were 2% per 2-month period?
2. What happens to the donation amount if the number of students increases?
3. How would the donation differ if the bursary only lasted for 50 years?
4. What if the bursary were awarded at the end of each year instead of the beginning?
5. How does compounding frequency impact the donation amount required?

**Tip:** Perpetuities rely heavily on the interest rate. Even small changes in the rate can significantly affect the donation amount required.

A company wants to set up a bursary at the university. The bursary should be such that it can forever give R6128 per year per student to 4 deserving students. If the bursaries are to be awarded at the beginning of each year (the first bursaries must be given to the students on the day that the company gives the university the donation) and the university earns interest at a rate of 1.4% per 2-month period, what amount should the company donate to the university? (Give your answer rounded to 2 decimal places.)

Learn how to calculate the required donation to fund perpetual bursaries for 4 students, each receiving R6128 annually, with a 1.4% interest compounded every 2 months. This step-by-step solution explains the concepts of perpetuity and compound interest, suitable for college-level financial mathematics students.

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