Question

Question 5 (7 marks)

An insurance policy requires you to make a single payment at the age of 30. In return, you can receive $100,000 every year starting from the age of 65 through 90 (i.e. the first payment will be made on the 65th birthday and the last on the 90th birthday). If the relevant interest rate is 10% compounded annually, how much will you pay for the insurance policy when you buy it on your 30th birthday?

Answer 1

Amount paid would be $ 35,858.24

Step-1:Value of Annuity at the age of 65
Value of annuity	=	Annual cash flow	*	Present value of annuity of 1
	=	$    1,00,000.00	*	10.07704
	=	$ 10,07,704.00
Working:
Present value of annuity of 1	=	((1-(1+i)^-n)/i)*(1+i)		Where,
	=	((1-(1+0.10)^-26)/0.10)*(1+0.10)	i	=	10%
	=	10.07704002			n	=	26
Step-2:Value at the age of 30
Value at the age of 30	=	Value at the age of 65	*	Present value of 1
	=	$ 10,07,704.00	*	0.035584
	=	$       35,858.24
Working:
Present value of 1	=	(1+i)^-n		Where,
	=	(1+0.10)^-35		i	=	10%
	=	0.035584103		n	=	35