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

46.

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
Amount = 10000 x (1+4/100)2
=10000 x (1+1/25)2 =10000 x (26/25) x (26/25) =10816

47.

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

48.

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/-

49.

Find the simple interest on Rs. 1920 at 45 % per annum for 3 months

A.) Rs. 196
B.) Rs. 216
C.) Rs. 206
D.) Rs. 306

Given
Principal : 1920
Rate of interest : 45
Number of months : 3
Simple interest for 1 year = pnr / 100
= ( 1920 x 1 x 45 ) / 100
= 864
Simple interest for 3 months = ( 3 / 12 ) x SI for 1 year
= ( 3 / 12 ) x 864
216

50.

A person receives a sum of Rs. 2100 as interest for investing some amount at 10% p.a compounding annually for 2 years. Find the amount invested at the beginning

A.) 10000
B.) 9000
C.) 10500
D.) 9500

Given Compound Interest = Rs.2100
Rate of Interest ( r ) = 10 % p.a
No.of years ( n ) = 2
To find , amount received at the beginning => principal
Compound Interest = P [ 1 + ( r / 100 )n- 1 ]
=> 2100 = P[ 1 + ( 10 / 100 )2- 1 ]
=> 2100 = P[ 1 + ( 1 / 10 )2- 1 ]
=> 2100 = P[ ( 11 / 10 )2- 1 ]
=> 2100 = P[ ( 121 / 100 ) - 1 ]
=> 2100 = P[ 21 / 100 ]
=> 2100 x ( 100 / 21 ) = P
Principal = Rs. 10000
Amount invested at the beginning = Rs. 10000

51.

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

52.

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

53.

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.) 10846
C.) 10816
D.) 10916

Given principal = 10000
No. of years = 2
Rate of interest = 4
Amount = P [ 1 + ( r / 100 )n]
= 10000 x [ 1 +( 4 / 100 )2]
= 10000 x ( 104 / 100 )2
= 10000 x ( 104 / 100 ) x ( 104 / 100 )
= 104 x 104
= 10816
Compound Interest = Amount - Principal

= 10816 - 10000
= 816

54.

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.

55.

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

56.

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.

57.

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/-

58.

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

59.

A person receives a sum of Rs. 210 as interest for investing some amount at 10% p.a compounding annually for 2 years. Find the amount invested at the beginning

A.) 1050
B.) 1000
C.) 850
D.) 950

Given
Compound interest received by the person ( C.I ) = Rs. 210
Rate of interest ( r ) = 10 %
Number of years ( n ) = 2 years
To find, Amount invested at the beginning = principal ( p )
Compound interest ( C.I ) = Amount - Principal
Amount = p ( 1 + r / 100 )n

=> C.I = p [ ( 1 + r / 100 )n- 1 ]
=> 210 = p [ ( 1 + 10 / 100 )2- 1 ]
=> 210 = p [ ( 110 / 100 )2- 1 ]
=> 210 = p [ ( 11 / 10 )2- 1 ]
=> 210 = p [ ( 121 / 100 ) - 1 ]
=> 210 = p [ ( 121 - 100 ) / 100 ]
=> 210 = p [ 21 / 100 ]
=> 210 x ( 100 / 21 ) = p
=> 1000 = p
The amount invested at the beginning = p = Rs.1000

60.

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.