Question

Step by Step calculations must be shown.

2.1. Sizwe has R75 000 to invest now for a period of 5 years. Bank A offers him an annual return of 7% whilst Bank B is prepared to offer him an annual return of 8%. How much more would he receive from Bank B compared to Bank A at the end of 5 years?

2.2. Jenet would like to receive R250 000 in 10 years’ time by making a single investment today. If her return on investment is 9% annually, how much must she invest today to achieve her goal?

2.3. Suppose you won the main prize in the lotto. Your prize is to receive R246 000 at the end of every year for the next 20 years. Your friend offers you a lump sum of R2 100 000 in exchange for these 20 years of receipts. If the annual interest rate is 10%, should you accept the offer? Motivate your answer

2.4. Charmaine invested R300 000 for 6 years at 10% interest compounded semi-annually. Use the appropriate formula to calculate the value of the investment at the end of 6 years.

2.5. John wants to have R1 000 000 in 6 years’ time so that he could purchase a luxurious yacht that he always wanted to own. How much money must he deposit annually to accumulate R1 000 000 in 6 years’ time if he can earn a return of 14%?

2.6. Calculate the effective interest rate (answer expressed to two decimal places) if the nominal rate of interest is 12% and interest is calculated quarterly.

Answer 1

2.1)	FV if deposit is made with Bank A = 75000*1.07^5 =	$      1,05,191.38
	FV if deposit is made with Bank B = 75000*1.08^5 =	$      1,10,199.61
	Amount received more from Bank B at EOY 5 =	$            5,008.23
2.2)	Amount to be deposted today is the PV of 250000 discounted for 10 years at 9% compounded annually = 250000/1.09^10 =	$      1,05,602.70
2.3)	The PV of the annuity of 246000 = 246000*(1.1^20-1)/(0.1*1.1^20) =	$   20,94,336.68
	AS the lump sum offered by the friend of $2100000 is
	more than the PV of the yearly payments, the offer
	of the friend should be accepted.
2.4)	FV of the investment = 300000*1.05^12 =	$      5,38,756.90
2.5)	1000000 is the FV of the annual deposits which
	constitute an annuity.
	Using the formula for finding the FV of annuity,
	the annual deposits required =
	= 1000000*0.14/(1.14^6-1) =	$      1,17,157.50
2.6)	EIR = 1.03^4-1 =	12.55%