Question

You would like to buy Tesla Model 3 car. The car loan requires payments of $600 per month for the first year and payments of $800 per month during the second year and also payments of 1,200 per month during the third year. The APR is 24% and payments begin in one month. What is the present value of this 3-year loan?

Answer 1

Computation of the Present value of the loan:

Given APR = 24%

Interest rate per month = 24% /12 = 2% per month

S.No	Installment Amount	Disc @ 2%	Present value
1	$600	0.9804	$588.24
2	$600	0.9612	$576.70
3	$600	0.9423	$565.39
4	$600	0.9238	$554.31
5	$600	0.9057	$543.44
6	$600	0.8880	$532.78
7	$600	0.8706	$522.34
8	$600	0.8535	$512.09
9	$600	0.8368	$502.05
10	$600	0.8203	$492.21
11	$600	0.8043	$482.56
12	$600	0.7885	$473.10
13	$800	0.7730	$618.43
14	$800	0.7579	$606.30
15	$800	0.7430	$594.41
16	$800	0.7284	$582.76
17	$800	0.7142	$571.33
18	$800	0.7002	$560.13
19	$800	0.6864	$549.14
20	$800	0.6730	$538.38
21	$800	0.6598	$527.82
22	$800	0.6468	$517.47
23	$800	0.6342	$507.32
24	$800	0.6217	$497.38
25	$1,200	0.6095	$731.44
26	$1,200	0.5976	$717.10
27	$1,200	0.5859	$703.03
28	$1,200	0.5744	$689.25
29	$1,200	0.5631	$675.73
30	$1,200	0.5521	$662.49
31	$1,200	0.5412	$649.50
32	$1,200	0.5306	$636.76
33	$1,200	0.5202	$624.27
34	$1,200	0.5100	$612.03
35	$1,200	0.5000	$600.03
36	$1,200	0.4902	$588.27
	Total		$20,905.97

We know that, the present value of the cash outflows is equal to the loan amount.

Hence the loan amount is $ 20905.97

The present value of 3 year loan is $ 20905.97

If you have any doubts,Please post a comment.

Thank you.Please rate it.