Question

Calculate the annual cash flows (annuity payments) from a fixed-payment annuity if the present value of the 25-year annuity is $1.9 million and the annuity earns a guaranteed annual return of 13 percent. The payments are to begin at the end of seven years.

Answer 1

Step-1:Calculation of value of fund 6 years from now
Future value of fund	=	Investment	x	Future value of 1 in 6 years
	=	$       19,00,000	x	2.081952
	=	$ 39,55,708.33
Working:
Future value of 1 in 6 years	=	(1+i)^n		Where,
	=	(1+0.13)^6		i	13%
	=	2.081951753		n	6
Step-2:Calculation of annual cash flows (Annuity)
Annual cash flows	=	Investment amount 6 years from now	/	Present value of annuity of 1
	=	$ 39,55,708.33	/	7.329985
	=	$    5,39,661.18
Working;
Present value of annuity of 1	=	(1-(1+i)^-n)/i		Where,
	=	(1-(1+0.13)^-25)/0.13		i	13%
	=	7.329984978		n	25
The question is based upon time value of money.
All the formulas are used based upon time value of money.