A deferred annuity is purchased with a lump sum amount of $308,273.17. Suppose money is worth...

A deferred annuity is purchased with a lump sum amount of $308,273.17. Suppose money is worth 5% compounded quarterly, and 13 years after the 5 year deferral period, the account is empty. Use this information to compute how much the annuity will pay per quarter after the deferral period.

Expert Solution

Future value of lumpsum is:

Future value	FV=	PV * (1+rs/m)^mN


Present value	PV=	308,273
Stated rate of interest	rs=	5.00%
Number of years	N=	5
Frequency of compounding per year	m=	4

Future value	FV=	308273.17 (1+ 0.05/4)^(54)

	FV=	395,217.6815

Payment per quarter is:

	Annuity payment=	P/ [ [1- (1+r)-n ]/r ]


P=	Present value	395,217.68
r=	Rate of interest per period
	Rate of interest per annum	5.0%
	Payments per year	4.00
	Rate of interest per period	1.250%




n=	number of payments:
	Number of years	13
	Payments per year	4.00

	number of payments	52


	Annuity payment=	395217.68/ [ (1- (1+0.0125)^-52)/0.0125 ]

	Annuity payment=	10,381.96

Payment per quarter is $10,381.96

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