Question

8. Consider the following two investment options: (1) Invest $1,000 and receive $110 at the end of each month for the next 10 months. (2) Invest $1,200 and receive $130 at the end of each month for the next 10 months. If this were your money, and you want to earn at least 12% interest on your money, which investment would you make, if any? Determine which alternative should be selected, based on Net Present Worth (NPW). Show all of your work and indicate which alternative you select, if any. (15 points)

Answer 1

Alternative 1:
Calculation of present worth
Present Value Of Annuity
= C*[1-(1+i)^-n]/i]
Where,
C= Cash Flow per period
i = interest rate per period
n=number of period
= $110[ 1-(1+0.01)^-10 /0.01]
= $110[ 1-(1.01)^-10 /0.01]
= $110[ (0.0947) ] /0.01
= $1,041.84
Present worth = $1041.84-1000
=$41.84
Alternative 2:
Present Value Of Annuity
= C*[1-(1+i)^-n]/i]
Where,
C= Cash Flow per period
i = interest rate per period
n=number of period
= $130[ 1-(1+0.01)^-10 /0.01]
= $130[ 1-(1.01)^-10 /0.01]
= $130[ (0.0947) ] /0.01
= $1,231.27
Present worth = $1231.27-1200
=$31.27
Alternative 1 should be selected as it is more worthy.

ALTERNATIVE METHOD

	Alternative 1:
	Year	Cash Flow	PV annuity at 1%	PV of Cash Flow
	0	-1000	1	$           -1,000.00
	1	110	0.99009901	$                108.91
	2	110	0.980296049	$                107.83
	3	110	0.970590148	$                106.76
	4	110	0.960980344	$                105.71
	5	110	0.951465688	$                104.66
	6	110	0.942045235	$                103.62
	7	110	0.932718055	$                102.60
	8	110	0.923483222	$                101.58
	9	110	0.914339824	$                100.58
	10	110	0.905286955	$                  99.58
	Present worth			$                  41.84
	Alternative 2:
	Year	Cash Flow	PV annuity at 1%	PV of Cash Flow
	0	-1200	1	$           -1,200.00
	1	130	0.99009901	$                128.71
	2	130	0.980296049	$                127.44
	3	130	0.970590148	$                126.18
	4	130	0.960980344	$                124.93
	5	130	0.951465688	$                123.69
	6	130	0.942045235	$                122.47
	7	130	0.932718055	$                121.25
	8	130	0.923483222	$                120.05
	9	130	0.914339824	$                118.86
	10	130	0.905286955	$                117.69
	Present worth			$                  31.27