Final answer:
The maximum amount of each bursary from the $750,000 fund earning 4.9% interest compounded semiannually is $3,675. This is calculated by determining the annual payout of the perpetuity and then dividing by five.
Step-by-step explanation:
The problem requires calculating the maximum amount of each bursary that can be awarded immediately from a fund intended to last in perpetuity. Since the fund is meant to last forever, we apply the concept of a perpetuity to determine the annual amount Ranger Oil can provide based on the interest generated by the fund.
The interest rate given is 4.9% compounded semiannually. The formula for the amount of a perpetuity is A = P × r, where A is the annual payout, P is the principal amount ($750,000), and r is the annual interest rate (as a decimal). Because the interest is compounded semiannually, we must adjust the interest rate by dividing it by 2, giving us 2.45% per period.
To find the total annual payout we use the formula: A = P × r/2, which in this case is A = $750,000 × 0.0245. Hence, A = $18,375 per year for bursaries. Since five bursaries are awarded each year, we divide this total by 5 to get the maximum amount of each bursary: $18,375 / 5 = $3,675.
Therefore, the maximum amount of each bursary that can be awarded immediately is $3,675.