question archive David Kapamagian borrowed money from a hank to finance a small fishing boat
David Kapamagian borrowed money from a hank to finance a small fishing boat
Subject:FinancePrice:3.87 Bought7
David Kapamagian borrowed money from a hank to finance a small fishing boat. The bank's terms allowed him to defer payments (including interest) on the loan for six months and to make 36 equal end-of-month payments thereafter. The original bank loan was for $4800, with an interest rate of 12% compounded monthly. After 16 monthly payments, David found himself in a financial bind and went to a loan company for assistance in lowering his monthly payments. Fortunately, the loan company offered to pay his debts in one lump sum if he would pay the company $104 per month for the next 36 months. What monthly rate of interest is the loan company charging on this transaction?
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Answer:
WN (‘1) Calculation of Equal Monthly Instalment on Original loan
P = $ 4800
‘i= 1 % per month
‘n = 36 Month
A= ‘i x (1+’i)n/ [(i+i)n -1]
By putting value in the above formula and by multiplying by P we get monthly instalment as under
Monthly instalment= 0.01 (1.01)36 / [ (1.01)36 -1]
Monthly instalment= 4800 x 0.033
Monthly instalment= $159.43
WN-(2) Calculation of loan amoritsation table for 16 Instalment
|
Period |
Principal |
Interest |
Instalment |
Principal Paid |
Outstanding Principal |
|
1 |
4800.00 |
48.00 |
159.43 |
111.43 |
4688.57 |
|
2 |
4688.57 |
46.89 |
159.43 |
112.54 |
4576.03 |
|
3 |
4576.03 |
45.76 |
159.43 |
113.67 |
4462.36 |
|
4 |
4462.36 |
44.62 |
159.43 |
114.81 |
4347.55 |
|
5 |
4347.55 |
43.48 |
159.43 |
115.95 |
4231.60 |
|
6 |
4231.60 |
42.32 |
159.43 |
117.11 |
4114.48 |
|
7 |
4114.48 |
41.14 |
159.43 |
118.29 |
3996.20 |
|
8 |
3996.20 |
39.96 |
159.43 |
119.47 |
3876.73 |
|
9 |
3876.73 |
38.77 |
159.43 |
120.66 |
3576.07 |
|
10 |
3756.07 |
37.56 |
159.43 |
121.87 |
3634.20 |
|
11 |
3634.20 |
36.34 |
159.43 |
123.09 |
3511.11 |
|
12 |
3511.11 |
35.11 |
159.43 |
124.32 |
3386.79 |
|
13 |
3386.79 |
33.87 |
159.43 |
125.56 |
3261.23 |
|
14 |
3261.23 |
32.61 |
159.43 |
126.82 |
3134.41 |
|
15 |
3134.41 |
31.34 |
159.43 |
128.09 |
3006.32 |
|
16 |
3006.32 |
30.06 |
159.43 |
129.37 |
2876.96 |
After the payment of 16 instalments principal balance is $ 2876.96
We know that from P (loan amount ) we will find out annual instalment by this formula
P= A x (1+i)n -1 ]/ i x (1+i)n
2876.96 = 104 x PVAF
PVAF= 27.663
By observing the table of PVAF
We get the interest rate= 18 %
Interest rate charged in the transaction = 18 %
