A person amortizes a loan of $17000 for a car with a 5 years loan at...

A person amortizes a loan of $17000 for a car with a 5 years loan at the rate of 6.5% compounded monthly. (a) Find the montly payments. The payments are of $ . (b) Find the total interest charges. The interest is $ . (c) Find the principal remaining after 2 years. The principal remaining is of $ .

Solutions

Expert Solution

(a) Find the montly payments

EMI = [P *I * (1+I)^N]/[(1+I)^N-1]

where

P =loan amount or Principal = 17000

I = Interest rate per monthb=6.5%/12
[To calculate rate per month: if the interest rate per annum is 14%, the per month rate would be 14/(12 x 100)]

N = the number of installments=5*12 = 60

EMI = [17000 *(.065/12)* (1+(.065/12))^60]/[(1+(.065/12))^60-1]

= (92.0833333333*1.38281732421)/1.38281732421 -1

= 127.334428604/.38281732421

= 332.62

(b) Find the total interest charges

Interest on mortgage = (EMI*no. of installments) - loan amount

= (332.62*60) - 17000

= 19957.2-17000

= 2,957.20

(c) Find the principal remaining after 2 years.

The principal remaining is of $ 10852.82. Loan amortisation schedule is below

Month	Opening Balance	Total Payment	interest paid	principal paid	end balance
1	17000.00	332.62	92.08	240.54	16759.46
2	16759.46	332.62	90.78	241.84	16517.62
3	16517.62	332.62	89.47	243.15	16274.47
4	16274.47	332.62	88.15	244.47	16030.01
5	16030.01	332.62	86.83	245.79	15784.22
6	15784.22	332.62	85.50	247.12	15537.09
7	15537.09	332.62	84.16	248.46	15288.63
8	15288.63	332.62	82.81	249.81	15038.83
9	15038.83	332.62	81.46	251.16	14787.67
10	14787.67	332.62	80.10	252.52	14535.15
11	14535.15	332.62	78.73	253.89	14281.26
12	14281.26	332.62	77.36	255.26	14026.00
13	14026.00	332.62	75.97	256.65	13769.35
14	13769.35	332.62	74.58	258.04	13511.31
15	13511.31	332.62	73.19	259.43	13251.88
16	13251.88	332.62	71.78	260.84	12991.04
17	12991.04	332.62	70.37	262.25	12728.79
18	12728.79	332.62	68.95	263.67	12465.12
19	12465.12	332.62	67.52	265.10	12200.02
20	12200.02	332.62	66.08	266.54	11933.48
21	11933.48	332.62	64.64	267.98	11665.50
22	11665.50	332.62	63.19	269.43	11396.07
23	11396.07	332.62	61.73	270.89	11125.18
24	11125.18	332.62	60.26	272.36	10852.82

jeff jeffy answered 1 year ago

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