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K Mautos is offering free credit on a new $110,000 car. You pay $2,0000 down and...

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Finance

K Mautos is offering free credit on a new $110,000 car. You pay$2,0000 down and then $3500 a month for the next 30 months. LemonMotors next door does not offer free credit but will give you$1,000 off the list price. If the rate of interest is 10% a year,which company is offering the better deal. Please help with anexcel.

Answer & Explanation Solved by verified expert
3.9 Ratings (455 Votes)

K.Mautos-

Interest rate = 10% per year = 10%/12 = 0.83% per month

We will discount each month's payment by dividing amount to be paid ($3500) by (1+0.83%)^n {n is no.of month).

Following excel shows amount, which is derived by dividing payment by discount factor. Discount factor =(1+0.83%)^n {n is no.of month).

Months Payment Discount Factor Amount
0 20000
1 3500 1.008 3471.189
2 3500 1.017 3442.615
3 3500 1.025 3414.277
4 3500 1.034 3386.172
5 3500 1.042 3358.298
6 3500 1.051 3330.653
7 3500 1.060 3303.237
8 3500 1.068 3276.045
9 3500 1.077 3249.078
10 3500 1.086 3222.333
11 3500 1.095 3195.807
12 3500 1.104 3169.501
13 3500 1.113 3143.41
14 3500 1.123 3117.535
15 3500 1.132 3091.872
16 3500 1.141 3066.421
17 3500 1.151 3041.179
18 3500 1.160 3016.145
19 3500 1.170 2991.317
20 3500 1.180 2966.694
21 3500 1.190 2942.273
22 3500 1.199 2918.053
23 3500 1.209 2894.032
24 3500 1.219 2870.21
25 3500 1.230 2846.583
26 3500 1.240 2823.151
27 3500 1.250 2799.912
28 3500 1.260 2776.864
29 3500 1.271 2754.005
30 3500 1.281 2731.335

Sum of all payments = 20,000 + 92,610 (sum of all payments discounted of 30 months) = $112,610

Lemon Motors- Payment to be made = 110,000 - 1000 = $109,000

So, Lemon Motors is better option.
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