Question

Kendra receives $900 now, $970 in 1 year, $1040 in 2 years, $1,110 in 3 years, and so on, until the final payment of $1600. Using an annual effective rate of interest of 9%, find (a) the present value of these payments at time 0; (b) the accumulated value at time 11 years.

Answer 1

1)	present value of these payments
	Year	Cash Flow	PV Factor	PV Of Cash Flow
	a	b	c=1/1.09^a	d=b*c
	0	$               900	1	$                 900.00
	1	$               970	0.917431193	$                 889.91
	2	$           1,040	0.841679993	$                 875.35
	3	$           1,110	0.77218348	$                 857.12
	4	$           1,180	0.708425211	$                 835.94
	5	$           1,250	0.649931386	$                 812.41
	6	$           1,320	0.596267327	$                 787.07
	7	$           1,390	0.547034245	$                 760.38
	8	$           1,460	0.50186628	$                 732.72
	9	$           1,530	0.46042778	$                 704.45
	10	$           1,600	0.422410807	$                 675.86
		Present value		$             8,831.22
2)	accumulated value at time 11 years.
	Year	Cash Flow	FV Factor	PV Of Cash Flow
	a	b		d=b*c
	0	$               900	2.36736	$             2,130.63
	1	$               970	2.17189	$             2,106.74
	2	$           1,040	1.99256	$             2,072.27
	3	$           1,110	1.82804	$             2,029.12
	4	$           1,180	1.67710	$             1,978.98
	5	$           1,250	1.53862	$             1,923.28
	6	$           1,320	1.41158	$             1,863.29
	7	$           1,390	1.29503	$             1,800.09
	8	$           1,460	1.18810	$             1,734.63
	9	$           1,530	1.09000	$             1,667.70
	10	$           1,600	1.00000	$             1,600.00
		Accumulated value		$           20,906.71