# Compound Interest : Aptitude Test (65 Questions with Explanation)

1.

What would be the compound interest on Rs.7700/- at 15 ¼% per annum for 2 years compounded annually

A.) Rs.2725.75/-
B.) Rs.2527.57/-
C.) Rs.2227.57/-
D.) Rs.2520.57/-

Principal = Rs. 7700/-
time = 2 years
rate = 15 ¼%
Amount = P(1+R/100)n
= 7700 × (1 + 61/(4 × 100)2)
= 7700 × [(1 + 61/400)2]
= 7700 × [(461/400)2)]
= 7700 × 461/400 × 461/400
= 7700 × 1.1525 × 1.1525
= 7700 × 1.32825625
= 10227.573125
C.I = 10227.573125 - 7700 = 2527.57/-

2.

Certain sum becomes 3 times it self at compound interest in 10 years. In how many years it becomes 9 times?

A.) 25 years
B.) 27 years
C.) 30 years
D.) 20 years

P(1 + R/100)10 = 3P
=> P(1 + R/100)10 = 3
Let P(1 + R/100)n = 9P
=> (1 + R/100)n = 9
=> 32 = [(1 + R/100)10]2
=> (1 + R/100)n => (1 + R/100)20
=> n = 20 Years.

3.

An amount at compound interest sums to Rs.17640/- in 2 years and to Rs.18522/- in 3 years at the same rate of interest. Find the rate percentage?

A.) 5%
B.) 6%
C.) 4%
D.) 10%

The difference of two successive amounts must be the simple interest in 1 year on
the lower amount of money.
S.I = 18522/- - 17640/- = Rs. 882/-
Rate of interest = (882/17640) × (100/1) => 8820/1764 = 5%
Principal = Amount/(1 + R/100)n
= 17640/(1 + 5/100)2
= 17640/(21/20 × 21/20)
= 17640/(1.05 × 1.05)
= 17640/1.1025
= 16000

4.

Certain loan amount was repaid in two annual installments of Rs.1331/- each. If the rate of interest be 10% per annum Compounded annually the sum borrowed was?

A.) Rs.121/-
B.) Rs.2130/-
C.) Rs.2310/-
D.) Rs.1331/-

Principal = (P.W of Rs. 1331/- due 1 year hence) + (P.W of Rs. 1331/- due 2 years hence)
= [1331/(1 + 10/100) + 1331/(1 + 10/100)2
= [1331/(110/100) + 1331/(110/100 × 110/100)]
= 13310/11 + 133100/121 = 1210 + 1100 = Rs.2310/-

5.

The difference between the compound interest and simple interest on a certain sum of money at 5% per annum for 2 years is 45. Then the original sum is?

A.) Rs.16000/-
B.) Rs.15000/-
C.) Rs.18000/-
D.) Rs.20000/-

For 2 years = (1002D)/R2
= (1002 × 45)/(5 × 5) = (10000 × 45)/25 = Rs.18000/-

6.

The Compound interest in a particular amount for the first year at 8% is Rs.50/-.The compound interest for 2 years at the same rate on the amount will be?

A.) Rs.52/-
B.) Rs.104/-
C.) Rs.102/-
D.) Rs.54/-

Rs.104/-

7.

The present worth of Rs.9826/- due 2 years at 6 ¼% per annum compound interest is:

A.) Rs.7804/-
B.) Rs.8704/-
C.) Rs.8760/-
D.) Rs.8504/-

Rs.8704/-

8.

The Compound interest of Rs.10240/- at 6 ¼% per annum for 2 years 292days is:

A.) Rs.1898/-
B.) Rs.1798/-
C.) Rs.1688/-
D.) Rs.1698/-

Rs.1898/-

9.

A person borrows a certain amount from his friend at the rate of 15% per annum compound interest, interest being compounded annually and agrees to return it in 2 equal yearly installments of Rs.529/- each. Find the amount borrow.

A.) Rs.820/-
B.) Rs.880/-
C.) Rs.860/-
D.) Rs.840/-

Rs.860/-

10.

Hari lended a sum of Rs.8000 for 20% per annum at compound interest then the sum of the amount will be Rs.13824 is obtained. After how many years he will get that amount?

A.) 2 years
B.) 1 year
C.) 4 years
D.) 3 years

Let Principal = P, Rate = R% per annum, Time = n years
When interest is compounded annually, total amount can be calculated by using the formula
Compound Amount = P ( 1 + R / 100)n
Given that, P = Rs.8000, R = 20% per annum
Compound Amount = Rs. 13824
We have to find the time period during which the amount will be Rs.13824
=> Rs.13824 = 8000 x (1 + 20/100)n
=> (13824 /8000) = (120 / 100)n
=> (24 / 20)3 = (12 / 10)n
=> (12 /10)3 = (12 /10 )n
Therefore, n = 3.
Hence the required time period is 3 years.

11.

What will be the amount if sum of Rs.10,00,000 is invested at compound interest for 3 years with rate of interest 11%, 12% and 13% respectively?

A.) Rs.14,04,816
B.) Rs.16,00,816
C.) Rs 12,14,816
D.) Rs. 11, 13,816

Given
Here, P = Rs.10,00,000, R1 = 11 , R2 = 12, R3 = 13.
Each rate of interest is calculated for one year.
Hence, N = 1 year.
Amount after 3 years,
= P(1 + R1/100) (1 + R2/100) (1 + R3/100)
= 10,00,000 × (1 + 11/100) × (1 + 12/100) × (1 + 13/100)
= 10,00,000 × (111/100) × (112/100) × (113/100)
= 111 x 112 x 113
= 14,04,816
Hence the total amount after 3 years is Rs.14,04,816

12.

Akarsh left a will of Rs. 16,400 for his two sons whose age are 17 and 18 years.They must get equal amounts when they are 20 years at 5% compound interest. Find the present share of the younger son.

A.) Rs. 7,000
B.) Rs. 8,000
C.) Rs. 5,000
D.) Rs. 11,000

Given, total amount (to be shared by two sons at the age of 20 on Compound interest) = Rs. 16,400
Let the Present share (Principal amount) for 17 year old son = "X"
Then the Present share (Principal amount) for 18 year old son = (16,400 - X)
To attain 20 years of age,
=> 17 year old son takes 3 years (N = 3 years on Compound interest)
=> 18 year old son takes 2 years (N = 2 years on Compound interest)
Given, Rate of interest (R) = 5%
Given that, at the age of 20, two sons get equal amount
=> Compound Amount of 17 year old son = Compound Amount of 18 year old son
W.K.T, Formula for Compound Amount = P [1 + (R/100)]^N
=> X (1 + 5/100)^3 = (16,400 - X) (1 + 5/100)^2
=> X (1 + 5/100) = (16,400 - X)
=> (105/100) X = (16,400 - X)
=> [(105/100) X] + X = 16,400
=> 205 X = 16,400 * 100
=> X = 16,40,000 / 205
=> X = 8,000
Therefore, Present share for 17 year old son = Rs. 8,000

13.

A sum of money is invested at 10% per annum compounding annually for 2 years. If the interest received is Rs. 210, find the principal.

A.) 2500
B.) 1000
C.) 1900
D.) 2100

Given, r = 10%
n = 2 years
Compound interest, C.I = Rs. 210
Compound Interest = Amount – Principal
=> C.I = P {[1 + (r/100)]n - 1}
=> 210 = P {[1 + (10/100)]2 - 1}
=> 210 = P {[1 + (1/10)]2 - 1}
=> 210 = P {[(10 + 1)/10]2 - 1}
=> 210 = P {[11/10]^2 - 1}
=> 210 = P {[121 / 100] – 1}
=> 210 = P {(121 – 100) / 100}
=> 210 = P {21 / 100}
=> P = (210 × 100) / 21
=> P = 1000 Rs.
Thus, Principal = Rs. 1000

14.

Rs. 10000 is borrowed at compound interest at the rate of 4 % annum. What will be the amount to be paid after 2 years?

A.) 10816
B.) 10800
C.) 10808
D.) 10826

Principal : P = 10000 Rs.
Rate of Interest : r = 4 %
Number of years : n = 2
Amount = P x (1 + r/100)n
Amount = 10000 x (1+4/100)2
=10000 x (1+1/25)2
=10000 x (26/25) x (26/25) =10816

15.

What would be the compound interest accrued on an amount of 5000 Rs. at the end of 2 years at the rate of 9 % per annum?

A.) 940.5
B.) 5940.5
C.) 5990.5
D.) 980.5

Given principal = 5000
No. of years = 2
Rate of interest = 9
Amount = P x (1+r/100)n,
We get Amount = 5000 x (1+9/100)2 = 5000 x (109/100) x (109/100) = 5940.5
Compound Interest, C. I = Amount - Principal = 5940.5 - 5000 = 940.5

16.

The difference between the simple interest on a certain sum at the rate of 10% p.a. for 2 years and compound interest which is compounded every 6 months is Rs.124.05 .What is the principal sum?

A.) Rs.12,000
B.) Rs.8000
C.) Rs.10,000
D.) Rs.6000

Let the sum be P
Compound Interest on P at 10% for 2 years when interest is compounded half-yearly
=P(1+ (R / 2)100) 2T−P= P(1+(10 / 2)100) 2× 2− P
=P(1+120)4−P=P(21 / 20) 4− P
Simple Interest on P at 10% for 2 years
=P × R × T /100
=P×10×2100
= P / 5
Then P[(1+5 / 100)4-1] - P x 10 x 2/100 = 124.05
⇒ P[(21/20)4 - 1 - 1/4] = 124.05
⇒ P[(194481/160000) - (6/5)] = 12405 /100
⇒ P[194481-192000 / 160000] = 12405 /100
⇒ P = [(12405/100) x (160000/2481)]
= 124.05 x 64.490
= 7999.9845
= 8000.

17.

The difference between compound interest and simple interest compounded annually on a certain sum of money for 2 years at 4% p.a. is Re.1 The sum (in Rs) is:

A.) 625
B.) 525
C.) 635
D.) 685

625

18.

There is 60% increase in an amount in 6 years at simple interest. What will be the compound interest of Rs.12,000 after 3 years at the same rate?

A.) Rs.3972
B.) Rs.2160
C.) Rs.3120
D.) Rs.6240

Let the Principal be, P = Rs. 100
Given, S.I = 60% of 100 = Rs. 60, n = 6 years
Then, Rate of Interest, r = (S.I × 100 )/ (p × n)
=> r = (60 × 100) / (100 × 6)
=> r = 10 % p.a
Now, P = Rs. 12,000, n = 3 years, r = 10% p.a
C.I = P {[1 + (r/100)]n - 1}
= 12,000 × {[1 + (10/100)]3-1}
= 12,000 × [(11/10)3-1]
= 12,000 × [(1331/1000) - 1]
= 12,000 × (331/1000)
= 12 × 331
= 3972
Thus, Compound Interest = Rs. 3972

19.

The compound interest on a certain sum for 2 years at 10% p.a. is Rs.525.The simple interest on the same sum for double the time at the half the rate percent per annum is:

A.) Rs.600
B.) Rs.500
C.) Rs.400
D.) Rs.800

Given, n = 2 years
r = 10 %
Compound interest (C.I) = Rs. 525
Compound interest (C.I) = P {[1 + (r/100)]n – 1}
=> P {[1 + (10/100)]2– 1} = 525
=> P {[1 + (1/10)]2 – 1} = 525
=> P {[11/10]2 – 1} = 525
=> P {[121/100] – 1} = 525
=> 21 × P / 100 = 525
=> P = 2500
Now for Simple Interest, S.I = p × n × r / 100
P = Rs. 2500
n = 4 years
r = 5%
S.I = (2500 × 4 × 5) / 100
=> S.I = 500 Rs.

20.

What will be compounded interest on a sum of Rs.25,000 after 3 years at the rate of 12 p.c.p.a.?

A.) Rs.9000.30
B.) Rs.10123.20
C.) Rs.9720
D.) Rs.9820

Rs.10123.20

21.

What would be the compound interest accrued on an amount of 6250 Rs. at the end of 2 years at the rate of 12 % per annum?

A.) 1570
B.) 1560
C.) 1580
D.) 1590

1590

22.

What would be the compound interest accrued on an amount of 10000 Rs. at the end of 2 years at the rate of 4 % per annum ?

A.) 816
B.) 916
C.) 826
D.) 846

Given principal = 10000
No. of years = 2
Rate of interest = 4
Amount = P x (1+r/100)n
we get Amount = 10000 x (1+4/100)2 = 10816
C.I = Amount - Principal = 10816 - 10000 = 816

23.

What would be the compound interest accrued on an amount of 6250 Rs. at the end of 2 years at the rate of 8 % per annum?

A.) 1060
B.) 1040
C.) 1020
D.) 1050

Given principal = 6250
No. of years = 2
Rate of interest = 8
Amount = P x (1+r/100)n,
We get Amount = 6250 x (1+8/100)2 = 7290
C.I = Amount - Principal = 7290 - 6250 = 1040

24.

What would be the compound interest accrued on an amount of 6500 Rs. at the end of 2 years at the rate of 15 % per annum?

A.) 2046.25
B.) 2056.25
C.) 2096.25
D.) 2076.25

Given principal = 6500
No. of years = 2
Rate of interest = 15
Amount = P x (1+r/100)n,
we get Amount = 6500 x (1+15/100)2 = 8596.25
C.I = Amount - Principal = 8596.25 - 6500 = 2096.25

25.

What would be the compound interest accrued on an amount of 5000 Rs. at the end of 2 years at the rate of 9 % per annum?

A.) 950.5
B.) 940.5
C.) 980.5
D.) 990.5

Given
Principal = 5000 No. of years = 2 Rate of interest = 9
Amount = P x (1+r/100)n
we get Amount
= 5000 x (1+9/100)2
= 5940.5
C.I = Amount - Principal
= 5940.5 - 5000
= 940.5.

26.

What would be the compound interest accrued on an amount of 12500 Rs. at the end of 3 years at the rate of 10 % per annum?

A.) 4137.5
B.) 4537.5
C.) 4237.5
D.) 4337.5

Given principal = 12500
No. of years = 3
Rate of interest = 10
Amount = P x (1+r/100)n,
We get Amount = 12500 x (1+10/100)3 = 16637.5
C.I = Amount - Principal = 16637.5 - 12500 = 4137.5

27.

What would be the compound interest accrued on an amount of 14000 Rs. at the end of 3 years at the rate of 5 % per annum?

A.) 2256.75
B.) 2206.75
C.) 2236.75
D.) 2216.75

Given
Principal = 14000 No. of years = 3 Rate of interest = 5
Amount = P x (1+r/100)n,
we get Amount = 14000 x (1+5/100)3 = 16206.75
C.I = Amount - Principal
= 16206.75 - 14000 = 2206.75.

28.

John invested an amount of Rs. 20000 for 2 years at compound interest at the rate of 6 % per annum. Find the amount he receives at the end of 2 years.

A.) 22472
B.) 22000
C.) 22372
D.) 22120

Given
Principal : P = 20000 Rs. Rate of Interest : r = 6 % Number of years : n = 2
Amount = P x (1 + r/100)n
Amount = 20000 x (1+6/100)2
= 20000 x (1+3/50)2
= 20000 x (53/50) x (53/50)
22472.

29.

What would be the compound interest accrued on an amount of 5000 Rs. at the end of 2 years at the rate of 16 % per annum?

A.) 1728
B.) 6528
C.) 6728
D.) ​1628

Given
principal = 5000
No. of years = 2
Rate of interest = 16
Amount = P x (1+r/100)n
we get Amount = 5000 x (1+16/100)2
= 5000 x (116 / 100)2
= 5000 x (116 / 100 ) x (116 / 100)
= 58 x 116
Amount = 6728
Compound interest = Amount - Principal

= 6728 - 5000
= 1728

30.

What would be the compound interest accrued on an amount of 14000 Rs. at the end of 3 years at the rate of 5 % per annum?

A.) 16206.75
B.) 2206.75
C.) 15216.75
D.) 16216.75

Given
principal = 14000
No. of years = 3
Rate of interest = 5
Amount = P x (1+r/100)n
we get Amount = 14000 x (1+5/100)3
= 14000 x (105 / 100)3
= 14000 x (21 / 20)3
= 14000 x (9261 / 8000)
= 64827 / 4
16206.75
compound interest = Amount - principal
=16206.75 -14000
=2206.75

31.

John invested an amount of Rs. 20000 for 2 years at compound interest at the rate of 6 % per annum. Find the amount he receives at the end of 2 years.

A.) 22120
B.) 22472
C.) 22000
D.) 22372

Principal : P = 20000 Rs.
Rate of Interest : r = 6 %
Number of years : n = 2
Amount = P x (1 + r/100)n
= 20000 x (1+6/100)2
= 20000 x (1+3/50)2
= 20000 x (53/50) x (53/50)
= 22472
Thus, Amount that Johnreceives at the end of 2 years = Rs.22472

32.

Rs. 10000 is borrowed at compound interest at the rate of 4 % per annum. What will be the amount to be paid after 2 years?

A.) 10816
B.) 10808
C.) 10800
D.) 10826

Principal : P = 10000 Rs.
Rate of Interest : r = 4 %
Number of years : n = 2
Amount = P x (1 + r/100)n
= 10000 x (1+4/100)2
=10000 x (1+1/25)2
=10000 x (26/25) x (26/25)
=10816
Thus, Amount to be paid after 2 years = Rs.10816

33.

What would be the compound interest accrued on an amount of 2500 Rs. at the end of 2 years at the rate of 10 % per annum?

A.) 3025
B.) 3035
C.) 3125
D.) 3045

Given principal = 2500
No. of years = 2
Rate of interest = 10
Amount = P x (1+r/100)n,
we get Amount = 2500 x (1+10/100)2 Ans : 3025

34.

What would be the compound interest accrued on an amount of 4500 Rs. at the end of 2 years at the rate of 10 % per annum ?

A.) 5435
B.) 5445
C.) 5665
D.) 5345

Given principal = 4500
No. of years = 2
Rate of interest = 10
Amount = P x (1+r/100)n,
We get Amount = 4500 x (1+10/100)2
Ans : 5445

35.

What would be the compound interest accrued on an amount of 11500 Rs. at the end of 2 years at the rate of 10 % per annum ?

A.) 13905
B.) 13915
C.) 13925
D.) 13965

Given
Principal = 11500 No. of years = 2 Rate of interest = 10
Amount = P x (1+r/100)n
we get Amount = 11500 x (1+10/100)2
= 11500 x ( 110 / 100 )2
= 115 x 11 x 11
= 115 x 121
Ans : 13915

36.

What would be the compound interest accrued on an amount of 5000 Rs. at the end of 2 years at the rate of 16 % per annum?

A.) 1728
B.) 6528
C.) 6928
D.) 6728

Given principal = 5000
No. of years = 2
Rate of interest = 16
Amount = P x (1+r/100)n,
= 5000 x (1+16/100)2
= 5000 x (1 + 4/25)2
= 5000 x (29 / 25)2
= 5000 x (841 / 625)
=6728
=>Amount = Rs.6728
Compound Interest = Amount - Principal

= 6728 - 5000
=1728
Thus,Compound Interest = Rs.1728

37.

What would be the compound interest accrued on an amount of 8000 Rs. at the end of 2 years at the rate of 5 % per annum?

A.) 8920
B.) 8820
C.) 8780
D.) 8810

Given principal = 8000.
No. of years = 2
Rate of interest = 5.
Amount = P x (1+r/100)n,
we get Amount = 8000 x (1+5/100)2 .
Ans : 8820

38.

The least number of complete years in which a sum of money put out at 20% compounded interest will be more than doubled is:

A.) 5
B.) 4
C.) 3
D.) 6

Given,
R = 20%
Compound interest (C.I) = P [1 + (r/100)]n
=> P [1 + (20/100)]n > 2P
=> (120/100)n > 2
=> (6/5)n > 2
=> {(6/5) × (6/5) × (6/5) × (6/5)} > 2
=> (6/5)4 = 2.0736 > 2
So, n = 4 years.

39.

A sum of money is borrowed and paid back in two annual instalments of Rs.882 each allowing 5% compound interest .The sum borrowed was:

A.) Rs.1640
B.) Rs.1620
C.) Rs.1680
D.) Rs.1700

Given
The sum borrowed
Present Worth of Rs.882 due 1 year + Present Worth of Rs.882 due 2 year
=> ( 882 ) / 1 + ( 5 / 100)1 + ( 882) / 1 + ( 5 / 100)1
=> (882 / 105 × 100 )1 + (882 / 105 × 100 )1
=> ( 882 /( 21 / 20 ) + ( 882 / (21 / 20)1
=> ( 882 × 20) / (21) + ( 882 × 20 × 20 / 21 × 21 )
=> 42 × 20 + 42 × 20 × 20 / 21
=> 840 + 2 × 20 × 20
=> 840 + 800
=> 1640
The sum borrowed = Rs.1640

40.

The population of a town is 196000. It increases by 7% in the 1st year and decreases by 5% in the 2nd year. What is the population of the town at the end of 2 years?

A.) 199234
B.) 201234
C.) 200234
D.) 189234

Initial population is 196000
In First Year, population increasesby 7%
New population
= (107/100) x 196000
= 107 × 196000 / 100
= 107 × 1960
209720
Population after 1 year = 209720
In second year, Population decreases by 5%,
New population
= (100 - 5)/100 x 209720
= (95/100) x 209720
= 19 * 10486
199234
Population after 2 years will be 199234.

41.

What would be the compound interest accrued on an amount of 2500 Rs. at the end of 2 years at the rate of 10 % per annum?

A.) 525
B.) 575
C.) 3125
D.) 3045

Given principal = 2500
No. of years = 2
Rate of interest = 10
Amount = P x (1+r/100)n,
=> Amount = 2500 x (1+10/100)2
= 2500 (11/ 10)2
= 2500 (121/ 100)
= 25 × 121
= 3025
So, Compound Amount = 3025
Compound Interest = Compound Amount - Principal

=> C.I = 3025 - 2500
=> C.I = 525 Rs.

42.

What would be the compound interest accrued on an amount of 6500 Rs. at the end of 2 years at the rate of 15 % per annum ?

A.) 8596.5
B.) 8596.25
C.) 8589.75
D.) 8589.25

Given principal = 6500
No. of years = 2
Rate of interest = 15
Amount = P x (1+r/100)n,
we get Amount = 6500 x (1+15/100)2
Ans : 8596.25

43.

What would be the compound interest accrued on an amount of 2500 Rs. at the end of 3 years at the rate of 10 % per annum?

A.) 827.5
B.) 3357.5
C.) 895.6
D.) 863.4

Given principal = 2500
No. of years = 3
Rate of interest (r) = 10
Amount = P x (1+r/100)n
=>Amount = 2500 x (1+10/100)3
= 2500 x (1+1/10)3
= 2500 x (11/10)3
= 2500 x (1331 / 1000)
=3327.5
=>Amount = Rs.3327.5
Compound interest = Amount - Principal
= 3327.5 - 2500
=827.5
Thus, theCompound interest = Rs.827.5

44.

What would be the compound interest accrued on an amount of 6250 Rs. at the end of 2 years at the rate of 8 % per annum?

A.) 7280
B.) 1040
C.) 1065
D.) 7390

Given, principal = 6250
No. of years = 2
Rate of interest = 8
Amount = P x (1+r/100)n,
=> Amount = 6250 x (1+8/100)2
= 6250 x (108 / 100)2
= 6250 x (108 / 100) x (108 / 100)
= 7290
Compound Interest = Amount - Principal
= 7290 - 6250
= 1040
Therefore, Compound Interest = Rs. 1040

45.

Hari lended a sum of Rs.8000 for 20% per annum at compound interest then the sum of the amount will be Rs.13824 is obtained. After how many years he will get that amount?

A.) 2 years
B.) 1 year
C.) 3 years
D.) 4 years

Let Principal = P, Rate = R% per annum, Time = n years
When interest is compounded annually, total amount can be calculated by using the formula
Compound Amount = P ( 1 + R / 100)n
Given that, P = Rs.8000, R = 20% per annum
Compound Amount = Rs. 13824
We have to find the time period during which the amount will be Rs.13824
=> Rs.13824 = 8000 x (1 + 20/100)n
=> (13824 /8000) = (120 / 100)n
=> (24 / 20)3 = (12 / 10)n
=> (12 /10)3 = (12 /10 )n
Therefore, n = 3.
Hence the required time period is 3 years.

46.

Akarsh left a will of Rs. 16,400 for his two sons whose age are 17 and 18 years.They must get equal amounts when they are 20 years at 5% compound interest. Find the present share of the younger son.

A.) Rs. 5,000
B.) Rs. 8,000
C.) Rs. 7,000
D.) Rs. 9,000

Given, total amount (to be shared by two sons at the age of 20 on Compound interest) = Rs. 16,400
Let the Present share (Principal amount) for 17 year old son = "X"
Then the Present share (Principal amount) for 18 year old son = (16,400 - X)
To attain 20 years of age,
=> 17 year old son takes 3 years (N = 3 years on Compound interest)
=> 18 year old son takes 2 years (N = 2 years on Compound interest)
Given, Rate of interest (R) = 5%
Given that, at the age of 20, two sons get equal amount
=> Compound Amount of 17 year old son = Compound Amount of 18 year old son
W.K.T, Formula for Compound Amount = P [1 + (R/100)]N
=> X (1 + 5/100)3 = (16,400 - X) (1 + 5/100)2
=> X (1 + 5/100) = (16,400 - X)
=> (105/100) X = (16,400 - X)
=> [(105/100) X] + X = 16,400
=> 205 X = 16,400 × 100
=> X = 16,40,000 / 205
=> X = 8,000
Therefore, Present share for 17 year old son = Rs. 8,000

47.

What will be the amount if sum of Rs.10,00,000 is invested at compound interest for 3 years with rate of interest 11%, 12% and 13% respectively?

A.) Rs.14,04,816
B.) Rs. 11, 13,816
C.) Rs 12,14,816
D.) Rs.16,00,816

Given
Here, P = Rs.10,00,000, R1 = 11 , R2 = 12, R3 = 13.
Each rate of interest is calculated for one year.
Hence, N = 1 year.
Amount after 3 years,
= P(1 + R1/100) (1 + R2/100) (1 + R3/100)
= 10,00,000 × (1 + 11/100) × (1 + 12/100) × (1 + 13/100)
= 10,00,000 × (111/100) × (112/100) × (113/100)
= 111 x 112 x 113
= 14,04,816
Hence the total amount after 3 years is Rs.14,04,816

48.

A sum of money is invested at 10% per annum compounding annually for 2 years. If the interest received is Rs. 210, find the principal.

A.) 2100
B.) 2500
C.) 1900
D.) 1000

Given, r = 10%
n = 2 years
Compound interest, C.I = Rs. 210
Compound Interest = Amount – Principal
=> C.I = P {[1 + (r/100)]n - 1}
=> 210 = P {[1 + (10/100)]2 - 1}
=> 210 = P {[1 + (1/10)]2 - 1}
=> 210 = P {[(10 + 1)/10]2 - 1}
=> 210 = P {[11/10]2 - 1}
=> 210 = P {[121 / 100] – 1}
=> 210 = P {(121 – 100) / 100}
=> 210 = P {21 / 100}
=> P = (210 × 100) / 21
=> P = 1000 Rs.
Thus, Principal = Rs. 1000

49.

What would be the compound interest accrued on an amount of 12500 Rs. at the end of 3 years at the rate of 10 % per annum?

A.) 4537.5
B.) 4137.5
C.) 6637.5
D.) 6647.5

Given principal = 12500
No. of years = 3
Rate of interest = 10
Amount = P x (1+r/100)n
= 12500 x (1+10/100)3
= 12500 x (11/10)3
= 12500 x (11/10)x (11/10)x (11/10)
= 16637.5
Compound Interest, C. I = Amount - Principal = 16637.5 - 12500 = 4137.5

50.

John invested an amount of Rs. 20000 for 2 years at compound interest at the rate of 6 % per annum. Find the amount he receives at the end of 2 years.

A.) 22472
B.) 22000
C.) 22372
D.) 22120

Given
Principal : P = 20000 Rs.
Rate of Interest : r = 6 %
Number of years : n = 2
Amount = P x (1 + r/100)n
=> Amount = 20000 x (1+6/100)2
= 20000 x (1+3/50)2
= 20000 x (53/50) x (53/50)
22472
Therefore, Amount received by John at the end of two years = Rs. 22472