Question

Computing a Present Value Involving an Annuity and a Single Payment You have decided to buy a used car. The dealer has offered you two options: a. Pay $500 per month for 20 months and an additional $12,000 at the end of 20 months. The dealer is charging an annual interest rate of 24%. b. Make a one-time payment of $14,906, due when you purchase the car. - In present value terms, which offer is a better deal? - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

Answer 1

OPTION : A
	Annual interest rate =		24%
	Monthly interest rate = 24% / 12 =		2%
CACLULATION OF THE NET PRESENT VALUE OF OPTIONA A
Years	Cash Outflow (A)	PVF OF $ 1 @ 2% (B)	Present Value (A XB)
1	$                         500	0.9804	$                     490
2	$                         500	0.9612	$                     481
3	$                         500	0.9423	$                     471
4	$                         500	0.9238	$                     462
5	$                         500	0.9057	$                     453
6	$                         500	0.8880	$                     444
7	$                         500	0.8706	$                     435
8	$                         500	0.8535	$                     427
9	$                         500	0.8368	$                     418
10	$                         500	0.8203	$                     410
11	$                         500	0.8043	$                     402
12	$                         500	0.7885	$                     394
13	$                         500	0.7730	$                     387
14	$                         500	0.7579	$                     379
15	$                         500	0.7430	$                     372
16	$                         500	0.7284	$                     364
17	$                         500	0.7142	$                     357
18	$                         500	0.7002	$                     350
19	$                         500	0.6864	$                     343
20	$                         500	0.6730	$                     336
20	$                   12,000	0.6730	$                 8,076
	Net Present Value		$               16,251
OPTION : B
Present value of one time payment at time of purchase of car =
	Cash Outflow	PV of $ 1	Present value
	$                   14,906	1	$               14,906
	Net Present value = $ 14,906
ANSWER =
In present value terms Option B is a better deal.