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1. Rs 7500 is borrowed at compound interest at the rate of 4% per annum. What will be the amount to be paid after 2 years?
  A.   Rs 8212
  B.  Rs 8112
  C.  Rs 8010
  D.  Rs 8212
     
   
View Answer

Shortcut:
If Principle = Rs P
Time = t years
Rate = r
and interest is compounded annually, then amount is given by
P
[
1 +
r / 100
]
t
Here, P = 7500, t = 2, r = 4
Using these values in shortcut, we get:
Amount = 7500
[
1 +
4 / 100
]
2 = 7500
[
1 +
1 / 25
]
2 =
7500 x 26 x 26 / 25 x 25
= 8112
Hence, the amount is Rs 8112.

2. Suraj invested an amount of Rs 16000 for two years at compounded interest and received an amount of Rs 17640 on maturity. What is the rate of interest?
  A.  5%
  B.  10%
  C.  7%
  D.  4%
     
   
View Answer

Shortcut:
If Principle = Rs P
Time = t years
Rate = r
and interest is compounded annually, then amount is given by
A = P
[
1 +
r / 100
]
t
Here, A = 17640, t = 2, P = 16000
Using these values in shortcut, we get:
17640 / 16000
=
[
1 +
r / 100
]
2
1764 / 1600
=
[
1 +
r / 100
]
2
Taking square root of both sides, we get:
42 / 40
− 1 =
r / 100

42 − 40 / 40
=
r / 100

2 / 40
=
r / 100

1 / 20
=
r / 100

r =
100 / 20
= 5
Hence, the rate is 5%.

3. Rs 7500 is borrowed at compound interest at the rate of 4% per annum. What will be the amount to be paid after 1 year, if interest is compounded half-yearly?
  A.  Rs 8803
  B.  Rs 7803
  C.  Rs 7703
  D.  Rs 7823
     
   
View Answer

Shortcut:
If Principle = Rs P
Time = t years
Rate = r
and interest is compounded half yearly, then amount is given by
A = P
[
1 +
r/2 / 100
]
2t
Here, t = 1, P = 7500, r = 4
Using these values in shortcut, we get:
A = 7500
[
1 +
4/2 / 100
]
2 x 1
= 7500
[
1 +
2 / 100
]
2
= 7500
[
1 +
1 / 50
]
2
= 7500
[
50 + 1 / 50
]
2
= 7500
[
51 / 50
]
2
= 7500 x
51 x 51 / 50 x 50
= 3 x 51 x 51 = 7803
Hence, the amount is Rs 7803.

4. Rs 7500 is borrowed at compound interest at the rate of 4% per annum. What will be the amount to be paid after 6 months, if interest is compounded quarterly?
  A.  Rs 7651
  B.  Rs 6650
  C.  Rs 7650.75
  D.  None of the above
     
   
View Answer

Shortcut:
If Principle = Rs P
Time = t years
Rate = r
and interest is compounded quarterly, then amount is given by
A = P
[
1 +
r/4 / 100
]
4t
Here, t = 6 months or 1/2 years, P = 7500, r = 4
Using these values in shortcut, we get:
A = 7500
[
1 +
4/4 / 100
]
4 x 1/2
= 7500
[
1 +
1 / 100
]
2
= 7500
[
100 + 1 / 100
]
2
= 7500
[
101 / 100
]
2
= 7500 x
101 x 101 / 100 x 100

= 75 x
101 x 101 / 100

=
765075 / 100

= 7650.75
Hence, the amount is Rs 7650.75.

5. Find the compound interest on Rs 2000 for 1
1 / 4
years at 10% per annum, the interest being payable quarterly.
  A.  Rs 262.81
  B.  Rs 252.84
  C.  Rs 272
  D.  Rs 260
     
   
View Answer

Shortcut:
If Principle = Rs P
Time = t years
Rate = r
and interest is compounded quarterly, then amount is given by
A = P
[
1 +
r/4 / 100
]
4t
Here, t = 5/4, P = 2000, r = 10
Using these values in shortcut, we get:
A = 2000
[
1 +
10/4 / 100
]
4 x 5/4
= 2000
[
1 +
5/2 / 100
]
5
= 2000
[
1 +
1 / 40
]
5
= 2000
[
40 + 1 / 40
]
5
= 2000
[
41 / 40
]
5
= 2000 x
41 x 41 x 41 x 41 x 41 / 40 x 40 x 40 x 40 x 40

=
41 x 41 x 41 x 41 x 41 / 2 x 4 x 4 x 40 x 40
= 2262.81
∴ the amount is Rs 2262.81.
Now, I = A − P = 2262.81 − 2000 = 262.81
Hence, the compound interest is Rs 262.81

6. If the interest is compounded annually, find the compound interest on Rs 2000 for 3 years at 10% per annum.
  A.  Rs 642
  B.  Rs 652
  C.  Rs 672
  D.  Rs 662
     
   
View Answer

Shortcut:
If Principle = Rs P
Time = t years
Rate = r
and interest is compounded annualy, then amount is given by
C.I = P
[
(
1 +
r / 100
)
t − 1
]

Here, t = 3, P = 2000, r = 10
Using these values in shortcut, we get:
C.I = 2000
[
(
1 +
10 / 100
)
3 − 1
]

= 2000
[
(
1 +
1 / 100
)
3 − 1
]

= 2000
[
(
10 + 1 / 100
)
3 − 1
]

= 2000
[
(
11 / 10
)
3 − 1
]

= 2000
[
(
11 x 11 x 11 / 10 x 10 x 10
)
− 1
]

= 2000
[
(
1331 / 1000
)
− 1
]

= 2000
[
(
1331 − 1000 / 1000
)
]

= 2000 x
331 / 1000
= 2 x 331 = 662
Hence, the compound interet is Rs 662

7. The compound interest on any sum at the rate of 5% for two years is Rs 512.5. Find the sum.
  A.  Rs 4000
  B.  Rs 5000
  C.  Rs 5100
  D.  Rs 4800
     
   
View Answer

Shortcut:
Let Principle is P
Time = t years
Rate = r
and interest is compounded annualy, then amount is given by
C.I = P
[
(
1 +
r / 100
)
t − 1
]

Here, C.I = 512.50, t = 3, P = ?, r = 5
Using these values in shortcut, we get:
512.5 = P
[
(
1 +
5 / 100
)
2 − 1
]

512.5 = P
[
(
1 +
1 / 20
)
2 − 1
]

512.5 = P
[
(
20 + 1 / 20
)
2 − 1
]

512.5 = P
[
(
21 / 20
)
2 − 1
]

512.5 = P
[
(
21 x 21 / 20 x 20
)
− 1
]

512.5 = P
[
(
441 / 400
)
− 1
]

512.5 = P
[
(
441 − 400 / 1000
)
]

512.5 = P x
41 / 400

P =
512.5 x 400 / 41

P =
5125 x 40 / 41

P = 125 x 40 = 5000
Hence, the principal is Rs 5000.

8. Find the amount on Rs 60,000, if the interest is compounded half-yearly at 4% for 1
1 / 2
years.
  A.  Rs 63772.48
  B.  Rs 63500
  C.  Rs 63672.48
  D.  Rs 63670
     
   
View Answer

Shortcut:
If Principle = Rs P
Time = t years
Rate = r
and interest is compounded half yearly, then amount is given by
A = P
[
1 +
r/2 / 100
]
2t
Here, t = 3/2, P = 60000, r = 4
Using these values in shortcut, we get:
A = 60000
[
1 +
4/2 / 100
]
2 x 3/2
= 60000
[
1 +
2 / 100
]
3
= 60000
[
1 +
1 / 50
]
3
= 60000
[
50 + 1 / 50
]
3
= 60000
[
51 / 50
]
3
= 60000 x
51 x 51 x 51 / 50 x 50 x 50

= 12 x
51 x 51 x 51 / 5 x 5

=
12 x 51 x 51 x 51 / 5 x 5
= 63672.48
Hence, the amount is Rs 63,672.48

9. What will be the compound interest acquired on a sum of Rs 12000 for 3 yers at the rate of 10% per annum?
  A.  Rs 3972
  B.  Rs 3872
  C.  Rs 3982
  D.  None of the above
     
   
View Answer

Shortcut:
Let Principle is P
Time = t years
Rate = r
and interest is compounded annualy, then amount is given by
C.I = P
[
(
1 +
r / 100
)
t − 1
]

Here, t = 3, P = 12000, r = 10
Using these values in shortcut, we get:
= 12000
[
(
1 +
10 / 100
)
3 − 1
]

= 12000
[
(
1 +
1 / 10
)
3 − 1
]

= 12000
[
(
10 + 1 / 10
)
3 − 1
]

= 12000
[
(
11 / 10
)
3 − 1
]

= 12000
[
(
11 x 11 x 11 / 10 x 10 x 10
)
− 1
]

= 12000
[
(
1331 / 1000
)
− 1
]

= 12000 x
1331 − 1000 / 1000

= 12000 x
331 / 1000

= 12 x 331 = 3972
Hence, the amount is Rs 3972.

10. What principal will amount to Rs 1352 in 2 years at 4% compound interest?
  A.  Rs 1240
  B.  Rs 1350
  C.  Rs 1150
  D.  Rs 1250
     
   
View Answer

Shortcut:
Let the Principle is P
Time = t years
Rate = r
and interest is compounded annually, then amount is given by
A = P
[
1 +
r / 100
]
t
Here, A = 1352, t = 2, r = 4
Using these values in shortcut, we get:
1352 / P
=
[
1 +
4 / 100
]
2
1352 / P
=
[
1 +
1 / 25
]
2
1352 / P
=
[
25 + 1 / 25
]
2
1352 / P
=
[
26 / 25
]
2
P =
1352 x 25 x 25 / 26 x 26

P = 2 x 25 x 25 = 1250
Hence, the principal is Rs 1250.

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