50 points
subhalaxmi took a loan of Rs.18000 fron surya finance to purchase a TV set. if the company charges compound interest at 12% p.a. during 1st year and 12 1/2 % during second year p.a. how much will she pay after 2yrs
Answers
Answered by
0
Rs.
18000
after
3
years at
12
%
compound interest
=
18000
(
1
+
12
100
)
3
=
18000
(
112
100
)
3
Let
x
be the annual installment.
Total effective repayment
=
x
after
2
years at
12
%
compound interest
+
x
after
1
year at
12
%
compound interest
+
x
=
x
(
1
+
12
100
)
2
+
x
(
1
+
12
100
)
+
x
=
x
(
112
100
)
2
+
x
(
112
100
)
+
x
=
x
[
(
112
100
)
2
+
(
112
100
)
+
1
]
With the third installment of
Rs.
x
, the entire money is paid back.
⇒
18000
(
112
100
)
3
=
x
[
(
112
100
)
2
+
(
112
100
)
+
1
]
x
=
18000
(
112
100
)
3
(
112
100
)
2
+
(
112
100
)
+
1
=
18000
(
100
112
)
+
(
100
112
)
2
+
(
100
112
)
3
=
18000
×
112
3
112
2
×
100
+
112
×
100
2
+
100
3
≈
7494
Each installment is approximately
Rs.
7494
.
This situation can now be generalized. Assume a loan of Rs. L is taken at R% compound interest per annum and this is repaid in n equal yearly instalments. Then each instalment can be given by
L
(
100
100
+
R
)
+
(
100
100
+
R
)
2
+
⋯
+
(
100
100
+
R
)
18000
after
3
years at
12
%
compound interest
=
18000
(
1
+
12
100
)
3
=
18000
(
112
100
)
3
Let
x
be the annual installment.
Total effective repayment
=
x
after
2
years at
12
%
compound interest
+
x
after
1
year at
12
%
compound interest
+
x
=
x
(
1
+
12
100
)
2
+
x
(
1
+
12
100
)
+
x
=
x
(
112
100
)
2
+
x
(
112
100
)
+
x
=
x
[
(
112
100
)
2
+
(
112
100
)
+
1
]
With the third installment of
Rs.
x
, the entire money is paid back.
⇒
18000
(
112
100
)
3
=
x
[
(
112
100
)
2
+
(
112
100
)
+
1
]
x
=
18000
(
112
100
)
3
(
112
100
)
2
+
(
112
100
)
+
1
=
18000
(
100
112
)
+
(
100
112
)
2
+
(
100
112
)
3
=
18000
×
112
3
112
2
×
100
+
112
×
100
2
+
100
3
≈
7494
Each installment is approximately
Rs.
7494
.
This situation can now be generalized. Assume a loan of Rs. L is taken at R% compound interest per annum and this is repaid in n equal yearly instalments. Then each instalment can be given by
L
(
100
100
+
R
)
+
(
100
100
+
R
)
2
+
⋯
+
(
100
100
+
R
)
harryp84:
it was waste of time fir u
for
Answered by
8
given principal p = 18000/-
for 1st year = 12 %
no of years n=1
amount after one year
p(1+R/100)
18000*1.12=20160
for 2nd year 12.5% and principal p = 20160/-
interest is annually .
amount after 2nd year
p(1+R/100)
20160=20160*1.125= 226800/-
for 1st year = 12 %
no of years n=1
amount after one year
p(1+R/100)
18000*1.12=20160
for 2nd year 12.5% and principal p = 20160/-
interest is annually .
amount after 2nd year
p(1+R/100)
20160=20160*1.125= 226800/-
Similar questions