Question

Part1: The Boxing Fund must pay an old boxer R18 000 every three months indefinitely. Money is worth 11.4% per year, compounded quarterly. What is the opening balance?

Part2: If the boxer decides to reschedule his compensation in three payments; the first payment now, the second payment twice the size of the first payment four years from now, and the third payment three times the size of the first payment nine years from now. The Boxing fund agrees on condition that the interest rate changes to 10.95% per year, compounded monthly. The amount to the nearest Rand that the boxer can expect to receive four years from now is?

Answer 1

Annual Rate of Interest	11.40%
Quarterly Discount Rate	(1+11.4%) ^ (1/4) - 1
Quarterly Discount Rate	2.74%
Quarterly Payment	18,000
Present Value of Quarterly Payment	Quarterly Payment Quarterly Discount Rate
Present Value of Quarterly Payment	657,972	Part I Answer
Annual Rate of Interest	10.95%
Monthly Compounded Rate	(1+10.95%) ^ (1/12) - 1
Monthly Compounded Rate	0.87%
Let Payment today be	x
Let Payment after 4 years be	2x	48 Months of Discounting
Let Payment after 9 years be	3x	108 Months of Discounting
48 Months of Discounting	1/(1 + 0.87%) ^ 48
48 Months of Discounting	0.6599
108 Months of Discounting	1/(1 + 0.87%) ^ 108
108 Months of Discounting	0.3925
Therefore,
657,972	=	x + 0.6599 * 2x + 0.3925 * 3x
657,972	=	3.4974x
x	=	188,132
Therefore, the boxer can receive the following payment schedule:
Today (x)	188,132
After 4 Years (2x)	376,263
After 9 Years (3x)	564,395