For the next 30 years, you will receive annual payments of $10,000/year. The difference in the...

For the next 30 years, you will receive annual payments of $10,000/year. The difference in the present value terms if you receive these payments at the beginning of each year rather than at the end of each year is closest to what value? Assume the discount rate is 6% APR

8150

8300

7850

8000

8450

Expert Solution

Present value of first series:

a	Present value of annuity=	P* [ [1- (1+r)-n ]/r ]

P=	Periodic payment	10,000.00
r=	Rate of interest per period
	Annual interest	6.00%
	Number of payments per year	1
	Interest rate per period	0.06/1=
	Interest rate per period	6.000%

n=	number of periods:
	Number of years	30
	Periods per year	1
	number of payments	30

	Present value of annuity=	10000* [ (1- (1+0.06)^-30)/0.06 ]
	Present value of annuity=	137,648.31

Present value of alternative series:

	Present value of annuity due=	P* [ [1- (1+r)-(n-1) ]/r ] + P


P=	Periodic payment	10,000.00


r=	Rate of interest per period:
	Annual rate of interest	6.00000%
	Frequency of payment	once in every 12 months
	Payments per year	12/ 12=	1
	Interest rate per period	0.06/1=	6.000%

n=	number of payments:
	Number of years	30
	Payments per year	1

	number of payments	30


	Present value of annuity=	10000* [ [1- (1+0.06)^-(30-1)]/0.06 ] +10000

	Present value of annuity=	145,907.21

Difference = 145,907.21 -137,648.31 = 8259

Answer is:

8300

please rate.

jeff jeffy answered 1 year ago

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