Question

Compute the present values of the following annuities first assuming that payments are made on the last day of the period and then assuming payments are made on the first day of the period: (Do not round intermediate calculations. Round your answers to 2 decimal places. (e.g., 32.16))

Payment Years. Interest Rate (Annual)

828.09. 8. 14%

9,468.26. 14. 7%

21,822.93. 24. 5%

71, 212.54. 5. 32%

Answer 1

Sol :

Payment	Years	Interest Rate (Annual)	present values payments made on the last day of the period	present values payments made on the first day of the period
828.09	8	14%	$3,841.40	$4,379.19
9,468.26	14	7%	$82,804.36	$88,600.67
21,822.93	24	5%	$301,126.79	$316,183.13
71,212.54	5	32%	$167,008.02	$220,450.58

Note - Annuity can be ordinary or due. Ordinary annuity occur at the end of the period and annuity due occur at the beginning of the period.

Present value of ordinary annuity (PVOA) = Annuity x (1- (1+r)^-n)/r

a) PVOA = 828.09 x1-(1+.14)^-8/.14

= 828.09 x 4.638863894

= $3841.40

b) PVOA = 9468.26 x 1-(1+.07)^-14/.07

= 9468.26 x 8.745467985

= $82804.36

c) PVOA = 21822.93 x 1-(1+.05)^-24/.05

= 21822.93 x 13.79864179

= $301126.79

d) PVOA = 71212.54 x 1-(1+.32)^-5/.32

= 71212.54 x 2.345205145

= $167008.02

Present value of annuity due (PVAD) = Annuity x (1+r) x (1-(1+r)^-n/r

a) PVAD = 828.09 x (1+.14) x (1-(1+.14)^-8/.14

= 828.09 x 1.14 x 4.638863894

= $4379.19

b) PVAD = 9468.26 x (1+.07) x (1-(1+.07)^-14/.07

= 9468.26 x 1.07 x 8.745467985

= $88600.67

c) PVAD = 21822.93 x (1+.05) x (1-(1+.05)^-24/.05

= 21822.93 x 1.05 x 13.79864179

= $316183.13

d) PVAD = 71212.54 x (1+.32) x (1-(1+.32)^-5/.32

= 71212.54 x 1.32 x 2.345205145

= $220450.58