A fund is to be donated by a wealthy man to provide annual scholarships to deserving students. The fund will grant P
5,000 each month for the first 5 years and P10,000 each month for another 5 years. If the fund earns a 12% interest p.a. compounded monthly, what is the amount of donation now.
5,000 each month for the first 5 years and P10,000 each month for another 5 years. If the fund earns a 12% interest p.a. compounded monthly, what is the amount of donation now.
Answers & Comments
Answer:
The amount of donation required to provide the scholarships is determined by the present value of the future streams of payments. The formula for computing the present value of an annuity is:
PV = C * [ 1 - (1 + R)^(-n ) ] / R
where PV is the present value, C is the monthly cash flow, R is the monthly interest rate and n is the number of years.
In the case of the fund, the monthly cash flow is P15,000 (P5,000 for the first 5 years and P10,000 for the next 5 years) and n is 10 years (60 months). The monthly interest rate is given as R = 0.12 (i.e., 12% per annum) divided by 12 (for month-on-month compounding).
So, plugging in the values in the formula, we get:
PV = P15,000 * [ 1 - (1 + 0.12)^(-10 ) ] / 0.12
= P15,000 * [ 1 - 0.851864661 ] / 0.12
= 9,556,102.28
The total amount of donation required is therefore:
Total donation = 10,000,000 P - 9,556,102.28 P
= 443,897.72 P
So, the wealthy man needs to donate P443,897.72 to fund the scholarships.