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11. Rs 800 at 5% per annum compound interest amount to Rs 882 in:
  A.  2 years
  B.  1 years
  C.  3 years
  D.  6 years
     
   
View Answer

Let the time is t A = P
[
1 +
r / 100
)
t
Here, t = ?, P = 800, r = 5, A = 882
Using these values in shortcut, we get:
882 = 800
[
1 +
5 / 100
]
t
882 = 800
[
1 +
1 / 20
]
t
882 / 800
=
[
20 + 1 / 20
]
t
882 / 800
=
[
21 / 20
]
t
[
441 / 400
=
[
21 / 20
]
t
[
21 / 20
]
2 =
[
21 / 20
]
t
∴ t = 2
Hence, the time is 2 years.

12. Rs 5000 is borrowed at Compund Interest at the rate of 2% for the first year, 4% for the second year and 5% for the third year. Find the amount to be paid after 3 years.
  A.  Rs 5589.2
  B.  Rs 5569.2
  C.  Rs 5669.2
  D.  Rs 5263.2
     
   
View Answer

shortcut:
When rate of interest is r1%, r2% and r3% for first year, second year and third year respectively, then amount is given by A = P
[
1 +
r1 / 100
]
x div class="frac" style=" font-size:40px;margin-top:-5px;">[1 +
r2 / 100
]
x div class="frac" style=" font-size:40px;margin-top:-5px;">[1 +
r3 / 100
]

Here, r1 = 2, r2 = 4, r3 = 5, P = 5000
Using these values in shortcut, we get:
A = 5000
[
1 +
2 / 100
]
x div class="frac" style=" font-size:40px;margin-top:-5px;">[1 +
4 / 100
]
x div class="frac" style=" font-size:40px;margin-top:-5px;">[1 +
5 / 100
]

A = 5000
[
100 + 2 / 100
]
x div class="frac" style=" font-size:40px;margin-top:-5px;">[
100 + 4 / 100
]
x div class="frac" style=" font-size:40px;margin-top:-5px;">[
100 + 5 / 100
]

A = 5000
[
102 / 100
]
x div class="frac" style=" font-size:40px;margin-top:-5px;">[
104 / 100
]
x div class="frac" style=" font-size:40px;margin-top:-5px;">[
105 / 100
]

A = 5000 x
102 x 104 x 105 / 100 x 100 x 100
A =
102 x 104 x 105 / 2 x 100
A = 51 x 104 x 1.05 = 5569.2
Hence, the amount is Rs 5569.2

13. At what rate per cent per annum will Rs 1000 amount to Rs 2197 in 3 years? The interest is compounded yearly.
  A.  33%
  B.  27%
  C.  30%
  D.  20%
     
   
View Answer

Let the amount is A, Principal is P & time is t Rate = n x 100
[
(
A / P
)
1/t x n − 1
]

If n = 1, then interest is compounded yearly.
If n = 2, then interest is compounded half-yearly.
If n = 4, then interest is compounded quarterly.
If n = 12, then interest is compounded monthly.
Here, P = 1000, A = 2197, t = 3
Using these values in shortcut where n = 1, we get:
Rate = 100
[
(
2197 / 1000
)
1/3 − 1
]

Rate = 100
[
(
13 / 10
)
3 x 1/3 − 1
]

Rate = 100
[
(
13 / 10
)
1 − 1
]

Rate = 100
[
13 − 10 / 10
]

Rate = 100
[
3 / 10
]

Rate = 10 x 3 = 30%
Hence, the rate is 30%.

14. At what rate percent compounded yearly will Rs 2500 amount to Rs 3600 in 2 years?
  A.  30%
  B.  10%
  C.  20%
  D.  25%
     
   
View Answer

Let the amount is A, Principal is P & time is t Rate = n x 100
[
(
A / P
)
1/t x n − 1
]

If n = 1, then interest is compounded yearly.
If n = 2, then interest is compounded half-yearly.
If n = 4, then interest is compounded quarterly.
If n = 12, then interest is compounded monthly.
Here, P = 2500, A = 3600, t = 2
Using these values in shortcut where n = 1, we get:
Rate = 100
[
(
3600 / 2500
)
1/2 − 1
]

Rate = 100
[
(
60 / 50
)
2 x 1/2 − 1
]

Rate = 100
[
60 − 50 / 50
]

Rate = 100
[
10 / 50
]

Rate = 2 x 10 = 20%
Hence, the rate is 20%.

15. Find the compound interest on Rs 4000 at 5% per annum, compounded yearly for 2
1 / 2
years.
  A.  Rs 520.25
  B.  Rs 535.50
  C.  Rs 500
  D.  Rs 510.75
     
   
View Answer

Let the amount is A, Principal is P, rate is r and time is given in the fraction like 2
1 / 2
, then Amount is given by Amount = P
[
1 +
r / 100
]
2 x
[
1 +
r/2 / 100
]

Here, P = 4000, r = 5, t = 2 1/2
Using these values in shortcut, we get:
Amount = 4000
[
1 +
5 / 100
]
2 x
[
1 +
5/2 / 100
]

Amount = 4000
[
1 +
1 / 20
]
2 x
[
1 +
1 / 40
]

Amount = 4000
[
20 + 1 / 20
]
2 x
[
40 + 1 / 40
]

Amount = 4000
[
21 / 20
]
2 x
[
41 / 40
]

Amount =
4000 x 21 x 21 x 41 / 20 x 20 x 40
Amount =
21 x 21 x 41 / 2 x 2
= 4520.25
∴ amount is Rs 4520.25
Now, CI = Amount − Principal = 4520.25 − 4000 = 520.25
Hence, the compound interest is Rs 520.25

16. A sum of money placed at compound interest doubles itself in 4 years. In how many years will it amount to 8 times itself?
  A.  7 years
  B.  10 years
  C.  13 years
  D.  12 years
     
   
View Answer

Shortcut:
A sum of money, placed at compound interest, becomes b times in t years and c times in z years. We calculate the value of z from the equation given below b
1 / t
= c
1 / z

Here, b = 3, t = 4, c = 8
Using these values in shortcut, we get:
2
1 / 4
= 8
1 / z

2
1 / 4
= 23 x
1 / z

⇒
1 / 4
=
3 / z
z = 12
Hence, the amount will becomes 8 times of itself in 12 years.

17. A sum of money at compound interest amounts to thrice itself in 3 years. In how many years will it be 9 times itself?
  A.  6 years
  B.  8 years
  C.  5 years
  D.  10 years
     
   
View Answer

Shortcut:
A sum of money, placed at compound interest, becomes b times in t years and c times in z years. We calculate the value of z from the equation given below b
1 / t
= c
1 / z

Here, b = 3, t = 3, c = 9
Using these values in shortcut, we get:
3
1 / 3
= 9
1 / z

3
1 / 3
= 3 2 x
1 / z

⇒
1 / 3
=
2 / z
z = 6
Hence, the amount will becomes 8 times of itself in 6 years.

18. If a sum of money at compound interest amounts to four times itself in 4 years, then in how many years will it be 8 times itself?
  A.  6 years
  B.  11 years
  C.  8 years
  D.  10 years
     
   
View Answer

Shortcut:
A sum of money, placed at compound interest, becomes b times in t years and c times in z years. We calculate the value of z from the equation given below b
1 / t
= c
1 / z

Here, b = 4, t = 4, c = 8
Using these values in shortcut, we get:
4
1 / 4
= 8
1 / z

22 x
1 / 4
= 2 3 x
1 / z

⇒
1 / 2
=
3 / z
z = 6
Hence, the amount will becomes 8 times of itself in 6 years.

19. At what rate per cent compound interest does a sum of money becomes four-fold in 2 years?
  A.  95%
  B.  100%
  C.  105%
  D.  110%
     
   
View Answer

Shortcut:
If a certain sum becomes 'a'times in 't' years the rate of compound interest r is equal to 100[(a)
1 / t
− 1]
Here, a = 4, t = 2
Using these values in shortcut, we get:
100[(4)
1 / 2
− 1]
100[(2)2 x
1 / 2
− 1]
100[2 − 1] = 100%
Hence, the rate is 100%.

20. At what rate per cent will the compound interest, does a sum of money becomes sixteen-fold in 2 years?
  A.  320%
  B.  100%
  C.  200%
  D.  300%
     
   
View Answer

Shortcut:
If a certain sum becomes 'a'times in 't' years the rate of compound interest r is equal to 100[(a)
1 / t
− 1]
Here, a = 16, t = 2
Using these values in shortcut, we get:
100[(16)
1 / 2
− 1]
100[(2)4 x
1 / 2
− 1]
100[(2)2 − 1]
100[4 − 1] = 100 x 3 = 300%
Hence, the rate is 300%.

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