Economy A family has borrowed
Economy
A family has borrowed $100,000 to purchase a new home. Theinterest rate is fixed at 12% compounded monthly over the 25-yearlife of the loan. Find the remaining balance on the loanimmediately after the payment listed Also find the amount ofinterest that comprises the payment listed. Payment 30
please answer in detail
Answer:
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 30th EMI weneed to first calculate EMI then prepare loan amortisationschedule.
If the loan amount is P, rate on interest (monthly is r, andloan 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 30th EMI is $982.16760
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