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.