Question

A construction company signed a loan contract at 6.73​%compoundedannually​, with the provision to pay​ $785 at the end of each month for three years.

​(a) What is the amount of the​ loan?

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

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

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

Answer 1

The formula is,

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

monthly amount=785

monthly interest rate=6.73%/12=0.5608%

n=number of months=12*3=36

785=loan amount*0.5608%*((1+0.5608%)^36)/[((1+0.5608%)^36)-1]

Loan amount=(139970.3/1.2230)*0.2230

=$25525.3

2. The outstanding balance at the end of 19 months=$12,694.68

3. The total principal amount paid in 19 months=$12,830.62

4. The total interest paid in 19 months=$$2084.38

Periods	Opening Balance	Monthly payment	Interest amount=(Opening Balance*0.5608%)	Principal amount=Monthly payment-Interest	Ending Balance=Opening Balance-Principal
1	25525.30	785	143.15	641.85	24883.46
2	24883.46	785	139.55	645.45	24238.01
3	24238.01	785	135.93	649.07	23588.95
4	23588.95	785	132.29	652.71	22936.24
5	22936.24	785	128.63	656.37	22279.87
6	22279.87	785	124.95	660.05	21619.83
7	21619.83	785	121.25	663.75	20956.08
8	20956.08	785	117.53	667.47	20288.61
9	20288.61	785	113.79	671.21	19617.39
10	19617.39	785	110.02	674.98	18942.41
11	18942.41	785	106.24	678.76	18263.65
12	18263.65	785	102.43	682.57	17581.08
13	17581.08	785	98.60	686.40	16894.68
14	16894.68	785	94.75	690.25	16204.43
15	16204.43	785	90.88	694.12	15510.31
16	15510.31	785	86.99	698.01	14812.30
17	14812.30	785	83.07	701.93	14110.37
18	14110.37	785	79.14	705.86	13404.50
19	13404.50	785	75.18	709.82	12694.68
			2084.38	12830.62