Question

a) On your sister’s 10th birthday, your parents want to invest a certain amount to enable her to withdraw R25 000 every six months from her 18th to her 24th birthday (both birthdays included). Calculate the sum they will have to invest if compounded interest is estimated at 12% per annum, compounded biannually.

b) What is the present value of a perpetuity that pays R4 800 per year if the first payment does not begin until four years later and if 12% per annum is the relevant discount rate?

c) if you want to withdraw R1 000 annually for the next nine years, and R1 500 annually in the three years thereafter with all payments occurring at the end of each year, determine the amount you should initially invest to fund your withdrawals given a rate of return of 7% per annum. Round your answer to the nearest Rand

Answer 1

a.	We need to invest Present value of future withdrawals.
	For 7 Years i.e. from 18th to 24th year on 10th birthday
	Rate =	12%	Compounded semi annually
	Value of funds at 18th birthday before withdrawal
	=25000 x PVAF(6%,14)
	=25000 x 9.29
	232374.60
	Investment need to be made today =
	=232374.6/(1+0.06)^(8x2)
	91473.40
b.	PV of perpetuity = A/i
	A is the annuity and I is the interest rate
	PV of perpetuity At the end of 4 years = 4800/0.12 = 40000
	PV of annuity today = 40000/(1+0.12)^4 = 25420.72
c.	Year	Cashflow	PVF @ 7%	Present Value
	1	1000	0.935	934.58
	2	1000	0.873	873.44
	3	1000	0.816	816.30
	4	1000	0.763	762.90
	5	1000	0.713	712.99
	6	1000	0.666	666.34
	7	1000	0.623	622.75
	8	1000	0.582	582.01
	9	1000	0.544	543.93
	10	1500	0.508	762.52
	11	1500	0.475	712.64
	12	1500	0.444	666.02
			Total	8656.41