Question

In: Finance

You want to buy a $18,500 car. The company is offering a 3% interest rate for...

You want to buy a $18,500 car. The company is offering a 3% interest rate for gour years. a. what will your minthly apyment be? Round to the nearest cent. b. assuming you pay that monthly amount for the entire 4 years, what is the total amount of money you will pay during thise 4 years for the car. C. How much interest will you pay during thise 4 years.

Solutions

Expert Solution

Given

Loan Amount (Present Value Annuity)= 18,500$

Interest rate (r)= 3% per anum

Tenure of the loan (n)= 4 years

Frequency of Payments (m) = monthly = 12

In order to calculate Monthly Payments, we have to use present value annuity formula which is as follows

PVA = Annuity *{(1-(1/(1+(r/m))^(m*n)))/(r/m)}

18500 = Annuity *{(1-(1/(1+(0.03/12))^(12*4)))/(0.03/12)}

18500 = Annuity *45.1787

Monthly Annuity = 18500/45.1787 = 409.4850

Monthly payment would be 410$

Interest = Beginning Balance * Interest Rate *1/12

Principal = Monthly Annuity - Interest

Ending Balance = Beginning Balance - Principal

Months Beginning Balance Interest Principal Monthly Payments Ending Balance
1 18500 46.25 ₹ 363.24 ₹ 409.49 ₹ 18,136.76
2 ₹ 18,136.76 45.34191238 ₹ 364.14 ₹ 409.49 ₹ 17,772.62
3 ₹ 17,772.62 44.43155453 ₹ 365.05 ₹ 409.49 ₹ 17,407.57
4 ₹ 17,407.57 43.5189208 ₹ 365.97 ₹ 409.49 ₹ 17,041.60
5 ₹ 17,041.60 42.60400548 ₹ 366.88 ₹ 409.49 ₹ 16,674.72
6 ₹ 16,674.72 41.68680287 ₹ 367.80 ₹ 409.49 ₹ 16,306.92
7 ₹ 16,306.92 40.76730725 ₹ 368.72 ₹ 409.49 ₹ 15,938.21
8 ₹ 15,938.21 39.8455129 ₹ 369.64 ₹ 409.49 ₹ 15,568.57
9 ₹ 15,568.57 38.92141405 ₹ 370.56 ₹ 409.49 ₹ 15,198.00
10 ₹ 15,198.00 37.99500497 ₹ 371.49 ₹ 409.49 ₹ 14,826.51
11 ₹ 14,826.51 37.06627986 ₹ 372.42 ₹ 409.49 ₹ 14,454.09
12 ₹ 14,454.09 36.13523293 ₹ 373.35 ₹ 409.49 ₹ 14,080.74
13 ₹ 14,080.74 35.20185839 ₹ 374.28 ₹ 409.49 ₹ 13,706.46
14 ₹ 13,706.46 34.26615041 ₹ 375.22 ₹ 409.49 ₹ 13,331.24
15 ₹ 13,331.24 33.32810317 ₹ 376.16 ₹ 409.49 ₹ 12,955.08
16 ₹ 12,955.08 32.3877108 ₹ 377.10 ₹ 409.49 ₹ 12,577.99
17 ₹ 12,577.99 31.44496745 ₹ 378.04 ₹ 409.49 ₹ 12,199.95
18 ₹ 12,199.95 30.49986725 ₹ 378.99 ₹ 409.49 ₹ 11,820.96
19 ₹ 11,820.96 29.5524043 ₹ 379.93 ₹ 409.49 ₹ 11,441.03
20 ₹ 11,441.03 28.60257268 ₹ 380.88 ₹ 409.49 ₹ 11,060.15
21 ₹ 11,060.15 27.65036649 ₹ 381.83 ₹ 409.49 ₹ 10,678.31
22 ₹ 10,678.31 26.69577978 ₹ 382.79 ₹ 409.49 ₹ 10,295.52
23 ₹ 10,295.52 25.73880661 ₹ 383.75 ₹ 409.49 ₹ 9,911.78
24 ₹ 9,911.78 24.779441 ₹ 384.71 ₹ 409.49 ₹ 9,527.07
25 ₹ 9,527.07 23.81767698 ₹ 385.67 ₹ 409.49 ₹ 9,141.40
26 ₹ 9,141.40 22.85350855 ₹ 386.63 ₹ 409.49 ₹ 8,754.77
27 ₹ 8,754.77 21.8869297 ₹ 387.60 ₹ 409.49 ₹ 8,367.17
28 ₹ 8,367.17 20.9179344 ₹ 388.57 ₹ 409.49 ₹ 7,978.61
29 ₹ 7,978.61 19.94651661 ₹ 389.54 ₹ 409.49 ₹ 7,589.07
30 ₹ 7,589.07 18.97267028 ₹ 390.51 ₹ 409.49 ₹ 7,198.56
31 ₹ 7,198.56 17.99638933 ₹ 391.49 ₹ 409.49 ₹ 6,807.07
32 ₹ 6,807.07 17.01766768 ₹ 392.47 ₹ 409.49 ₹ 6,414.60
33 ₹ 6,414.60 16.03649923 ₹ 393.45 ₹ 409.49 ₹ 6,021.15
34 ₹ 6,021.15 15.05287786 ₹ 394.43 ₹ 409.49 ₹ 5,626.72
35 ₹ 5,626.72 14.06679743 ₹ 395.42 ₹ 409.49 ₹ 5,231.30
36 ₹ 5,231.30 13.0782518 ₹ 396.41 ₹ 409.49 ₹ 4,834.89
37 ₹ 4,834.89 12.0872348 ₹ 397.40 ₹ 409.49 ₹ 4,437.50
38 ₹ 4,437.50 11.09374027 ₹ 398.39 ₹ 409.49 ₹ 4,039.10
39 ₹ 4,039.10 10.09776199 ₹ 399.39 ₹ 409.49 ₹ 3,639.72
40 ₹ 3,639.72 9.099293776 ₹ 400.39 ₹ 409.49 ₹ 3,239.33
41 ₹ 3,239.33 8.098329387 ₹ 401.39 ₹ 409.49 ₹ 2,837.95
42 ₹ 2,837.95 7.094862588 ₹ 402.39 ₹ 409.49 ₹ 2,435.55
43 ₹ 2,435.55 6.088887121 ₹ 403.40 ₹ 409.49 ₹ 2,032.16
44 ₹ 2,032.16 5.080396715 ₹ 404.40 ₹ 409.49 ₹ 1,627.75
45 ₹ 1,627.75 4.069385084 ₹ 405.42 ₹ 409.49 ₹ 1,222.34
46 ₹ 1,222.34
jeff jeffy answered 2 years ago
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