Question

Travis bought a new Corvette Z06 for $100,000. He got a 60 month loan for $77800 at a nominal rate of 8.125% per month, with uniform monthly payments starting one month from the date of purchase. What were his monthly car payments? $  
after 24 months how much would he still owe? $  
He sold the car at the end of 36 months for $60,000. What was the payoff. $  (remember to add the last payment) How much of his twelfth payment was interest? $  
How much of his twelfth payment was equity? $

Answer 1

(a)

Monthly nominal interest rate = 8.125% / 12 = 0.6771%

Monthly payment ($) = Loan amount / P/A(0.6771%, 60) = 77,800 / 49.1720** = 1,582.20

(b)

After 24 months, number of months left = 60 - 24 = 36

Amount owed (including principal (equity) and interest) = $1,582.20 x 36 = $56,959.20

(c)

Total loan payment in 36 months (including principal (equity) and interest) = $56,959.20

Payoff = Sale price of car - Total loan payment in 36 months = $(60,000 - 56,959.2) = $3,040.8

(d) Loan amortization schedule for first 12 months is as follows.

Working notes:

(i) Interest payment in month N = Beginning balance in month N x 0.006771

(b) Principal payment in month N = $1,582.2 - Interest payment in month N

Month	Beginning balance ($)	Monthly Payment ($)	Interest Payment ($)	Principal Payment ($)	Ending Balance ($)
1	77,800	1,582.20	526.78	1,055.42	76,218
2	76,218	1,582.20	516.07	1,066.13	74,636
3	74,636	1,582.20	505.36	1,076.84	73,053
4	73,053	1,582.20	494.64	1,087.56	71,471
5	71,471	1,582.20	483.93	1,098.27	69,889
6	69,889	1,582.20	473.22	1,108.98	68,307
7	68,307	1,582.20	462.51	1,119.69	66,725
8	66,725	1,582.20	451.79	1,130.41	65,142
9	65,142	1,582.20	441.08	1,141.12	63,560
10	63,560	1,582.20	430.37	1,151.83	61,978
11	61,978	1,582.20	419.65	1,162.55	60,396
12	60,396	1,582.20	408.94	1,173.26	58,814
TOTAL		18,986.40	5,614.34	13,372.06

Interest in 12th payment = $5,614.34

Principal (equity) in 12th payment = $13,372.06

**P/A(r%, N) = [1 - (1 + r)^-N] / r

P/A(0.6771%, 60) = [1 - (1.006771)^-60] / 0.006771 = (1 - 0.6671) / 0.006771 = 0.3329 / 0.006771 = 49.1720