Question

Economy

A family has borrowed $100,000 to purchase a new home. The interest rate is fixed at 12% compounded monthly over the 25-year life of the loan. Find the remaining balance on the loan immediately after the payment listed Also find the amount of interest that comprises the payment listed. Payment 30   

please answer in detail

Answer 1

If the total loan amount is P, periodic interest rate is (i), and total loan period is (t), and number of emi paid is [c]

we can find remaining loan amount (B) using below formula

B = P [(1 + i) ^n - (1 + i) ^c]/ [(1 + i) ^n -1]

Where,

                  Loan amount (P) = $100000

                  Interest rate = 1% per period

                  Total loan term (n) = 300 months

                  Loan paid for period [c] = 30 months

Let's put all the values in the formula

B = 100000* [(1 + 0.01) ^300 - (1 + 0.01) ^30]/ [(1 + 0.01) ^300 - 1]

    = 100000* [(1.01) ^300 - (1.01) ^30]/ [(1.01) ^300 - 1]

    = 100000* [19.7884662619 - 1.3478489153]/ [19.7884662619 - 1]

    = 100000* [18.4406173466/ 18.7884662619]

    = 100000* 0.9814860399

    = 98148.6

So remaining loan amount is $98148.6

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To calculate the interest part in the 30^th EMI we need to first calculate EMI then prepare loan amortisation schedule.

If the loan amount is P, rate on interest (monthly is r, and loan term is n the EMI will be

EMI= P*r[(1 +r)^n]/ [(1+ r)^n- 1]

= 100000*0.01[(1 +0.01)^300]/ [(1+ 0.01)^300- 1]

= 1000[(1.01)^300]/ [(1.01)^300- 1]

= 1000[19.79]/ [19.7884662619245- 1]

= 1000[19.79]/ [18.7884662619245]

= 1000[1.05330577409105]

= 1053.31

So EMI will be $1053.31

EMI	Loan balance	EMI	Interest (Loan * interest)	Principle (EMI - Interest)	Loan balance
1	1,00,000.00000	1,053.31000	1,000.00000	53.31	99946.69
2	99,946.69000	1,053.31000	999.46690	53.84	99892.85
3	99,892.84690	1,053.31000	998.92847	54.38	99838.47
4	99,838.46537	1,053.31000	998.38465	54.93	99783.54
5	99,783.54002	1,053.31000	997.83540	55.47	99728.07
6	99,728.06542	1,053.31000	997.28065	56.03	99672.04
7	99,672.03608	1,053.31000	996.72036	56.59	99615.45
8	99,615.44644	1,053.31000	996.15446	57.16	99558.29
9	99,558.29090	1,053.31000	995.58291	57.73	99500.56
10	99,500.56381	1,053.31000	995.00564	58.30	99442.26
11	99,442.25945	1,053.31000	994.42259	58.89	99383.37
12	99,383.37204	1,053.31000	993.83372	59.48	99323.90
13	99,323.89576	1,053.31000	993.23896	60.07	99263.82
14	99,263.82472	1,053.31000	992.63825	60.67	99203.15
15	99,203.15297	1,053.31000	992.03153	61.28	99141.87
16	99,141.87450	1,053.31000	991.41874	61.89	99079.98
17	99,079.98324	1,053.31000	990.79983	62.51	99017.47
18	99,017.47308	1,053.31000	990.17473	63.14	98954.34
19	98,954.33781	1,053.31000	989.54338	63.77	98890.57
20	98,890.57119	1,053.31000	988.90571	64.40	98826.17
21	98,826.16690	1,053.31000	988.26167	65.05	98761.12
22	98,761.11857	1,053.31000	987.61119	65.70	98695.42
23	98,695.41975	1,053.31000	986.95420	66.36	98629.06
24	98,629.06395	1,053.31000	986.29064	67.02	98562.04
25	98,562.04459	1,053.31000	985.62045	67.69	98494.36
26	98,494.35503	1,053.31000	984.94355	68.37	98425.99
27	98,425.98858	1,053.31000	984.25989	69.05	98356.94
28	98,356.93847	1,053.31000	983.56938	69.74	98287.20
29	98,287.19786	1,053.31000	982.87198	70.44	98216.76
30	98,216.75983	1,053.31000	982.16760	71.14	98145.62

So interest in the 30^th EMI is $982.16760

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