Question

A construction company signed a loan contract at 4.18​% compounded annually​, with the provision to pay ​$455 at the end of each month for three years.

​(a) What is amount of the​ loan?

​(b) How much will be owed at the end of twenty ​months?

​(c) How much of the principal will be repaid within the first twenty ​months?

​(d) How much interest is paid during the first twenty months?

Answer 1

The formula is,

a. Monthly payment=Loan amount*monthly interest rate*((1+monthly interest rate)^n)/[((1+monthly interest rate)^n)-1]

monthly payment=455

monthly interest rate=4.18%/12=0.3483%

n=total number of months=3*12=36

455=loan amount*0.3483%*((1+0.3483%)^36)/[((1+0.3483%)^36)-1]

loan amount=(455/0.3483%)*[((1+0.3483%)^36)-1]/((1+0.3483%)^36)

loan amount=130622*0.133355/1.133355=$153,69.48

Please find the below amortization schedule with formulas, how I arrived at

b. The outstanding balance at the end of twenty months=$7068.80

c. The total principal paid in twenty months=$8300.68

d. The total interest paid in twenty months=$799.32

Periods	Opening Balance	Monthly payment	Interest amount=(Opening Balance*0.3483%)	Principal amount=monthly payment-Interest	Ending Balance=Opening Balance-Principal
1	15369.48	455.00	53.53	401.47	14968.01
2	14968.01	455.00	52.13	402.87	14565.15
3	14565.15	455.00	50.73	404.27	14160.88
4	14160.88	455.00	49.32	405.68	13755.20
5	13755.20	455.00	47.91	407.09	13348.11
6	13348.11	455.00	46.49	408.51	12939.60
7	12939.60	455.00	45.07	409.93	12529.67
8	12529.67	455.00	43.64	411.36	12118.31
9	12118.31	455.00	42.21	412.79	11705.52
10	11705.52	455.00	40.77	414.23	11291.29
11	11291.29	455.00	39.33	415.67	10875.61
12	10875.61	455.00	37.88	417.12	10458.49
13	10458.49	455.00	36.43	418.57	10039.92
14	10039.92	455.00	34.97	420.03	9619.89
15	9619.89	455.00	33.51	421.49	9198.40
16	9198.40	455.00	32.04	422.96	8775.43
17	8775.43	455.00	30.56	424.44	8351.00
18	8351.00	455.00	29.09	425.91	7925.09
19	7925.09	455.00	27.60	427.40	7497.69
20	7497.69	455.00	26.11	428.89	7068.80
			799.32	8300.68