Question

You deposit $11,200 annually into a life insurance fund for the next 10 years, at which time you plan to retire. Instead of a lump sum, you wish to receive annuities for the next 20 years. What is the annual payment you expect to receive beginning in year 11 if you assume an interest rate of 6 percent for the whole time period? (Do not round intermediate calculations. Round your answer to 2 decimal places. (e.g., 32.16))

Annuities per year over the next 20 years =

Answer 1

Annuities per year over the next 20 years = $ 12,870.61

Step-1:Future value of annual cash flow for next 10 years
Future value		=	Annual cash flow	*	Future value of annuity of 1
		=	$           11,200	*	13.18079
		=	$ 1,47,624.90
Working:
Future value of annuity of 1		=	(((1+i)^n)-1)/i			Where,
		=	(((1+0.06)^10)-1)/0.06			i	=	6%
		=	13.18079494			n	=	10
Step-2:Annual cash flow for next 20 years
Annual cash flow		=	Present value	/	Present value of annuity of 1
		=	$ 1,47,624.90	/	11.46992
		=	$     12,870.61
Working:
Present value of annuity of 1		=	(1-(1+i)^-n)/i		Where,
		=	(1-(1+0.06)^-20)/0.06		i	=	6%
		=	11.46992122		n	=	20