Question

Under the NBA deferred compensation plan, payments made at the end of each year accumulate up to retirement and then retirees are given two options. Option 1 allows the retiree to select the amount of the annual payment to be received, and option 2 allows the retiree to specify over how many years payments are to be received. Assume Hardaway has had $6,100 deposited at the end of each year for 30 years, and that the long-term interest rate has been 7%. (FV of $1, PV of $1, FVA of $1, PVA of $1, FVAD of $1 and PVAD of $1) (Use appropriate factor(s) from the tables provided.)

Required:
a. How much has accumulated in Hardaway's deferred compensation account?
b. How much will Hardaway be able to withdraw at the beginning of each year if he elects to receive payments for 16 years?
c. How many years will Hardaway be able to receive payments if he chooses to receive $66,000 per year at the beginning of each year?

Answer 1

a

FV of annuity	=	P * [ (1+r)^n -1 ]/ r
Periodic payment	P=	$                6,100.00
rate of interest per period	r=
Rate of interest per year		7.0000%
Payment frequency		Once in 12 months
Number of payments in a year		1.00
rate of interest per period		0.07*12/12	7.0000%
Number of periods
Number of years		30
Number of payments in a year		1
Total number of periods	n=	30
FV of annuity	=	6100* [ (1+0.07)^30 -1]/0.07
FV of annuity	=	576,210.80

Answer is:

576,210.80

b

Payment from today	=	FV/ [(1+r) * [ (1+r)^n -1 ]/r]
Future value	FV=	576,210.80
Rate of interest per period	r=
Rate of interest per year		7.0000%
Payment frequency		Once in 12 months
Number of payments in a year		1.00
rate of interest per period		0.07*12/12	7.0000%
Number of periods	n=
Number of years		16
Number of payments in a year		1
Total number of periods	n=	16
Annuity due	=	576210.8/[ (1+0.07) * 8 [ (1+0.07)^ 16 -1] /0.07]
	=	19,309.87

Answer is:

19,309.87

c

n	Number of payments required =	Log [ 1/ [1 - PV× r/ P] ]/ Log(1+r)
PV =	Present value	$                       510,210.80
P=	Periodic payment	66,000.00
r=	Rate of interest per period
	Annual interest	7.00%
	Number of payments per year	1
	Interest rate per period	0.07/1=
	Interest rate per period	7.000000%
	Number of payments =	Log [ 1/ (1- 510210.8 × 0.07/66000) ]/ Log( 1+ 0.07)
n=	Number of payments =	11.51

Total payments = 11.51 + 1 payment at beginning = 12.51 years

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