RRB NTPC - Compound Interest : Aptitude Test (65 Questions with Explanation)

1.

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

Answer: Option 'A'

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

2.

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

Answer: Option 'A'

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

3.

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

Answer: Option 'D'

1590

4.

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

Answer: Option 'A'

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.

5.

Mr. Joshua invested Rs 15,000 divided into two different schemes A and B at S.I of 5% and 10%. If the total amount of the simple interest earned in 2 years is 2500, What was the amount invested in scheme B. 

   A.) 25,000
   B.) 10,000
   C.) 15,500
   D.) 30,000

Answer: Option 'B'

Given Total Principal = Rs. 15,000
Number of years = 2 years
Total S.I at the end of 2 years = Rs. 2500

For scheme A, Amount invested = x Rs.
Rate of interest, r = 5%

For scheme B, Amount invested= (15,000 - x) Rs.
Rate of interest, r = 10%

W.K.T: S.I = p * n * r / 100
=> S.I for scheme A + S.I for scheme B = Rs. 2500
=> {(x * 2 * 5)/ 100} + {(15,000 - x) * 2 * 10/ 100} = 2500
=> (x / 10) + 2(15,000 - x)/ 10 = 2500
=> (x/ 10) + (30,000 - 2x) /10 = 2500
=> x + 30,000 - 2x = 2500 * 10
=> 30,000 - x = 25000
=> x = 30,000 - 25,000
=> x= 5,000

For scheme B, Amount invested = (15,000 - x) Rs.
= 15,000 - 5,000
= 10,000 Rs.

6.

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

Answer: Option 'B'

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

7.

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.) 945
   B.) 5665
   C.) 5445
   D.) 435

Answer: Option 'A'

Given principal = 4500
No. of years = 2
Rate of interest = 10
Amount = P [ 1 + ( r / 100 ) ]n
= 4500 x [ 1 + ( 10 / 100 ) ]2
= 4500 x [ 1 + ( 1 / 10 ) ]2
= 4500 x [ 11 / 10 ]2
= 4500 x [ 121 / 100 ]
Amount = 5445
Compound interest = Amount - principal

= 5445 - 4500
= 945 Rs

8.

Find the simple interest on Rs. 1300 at 10 % per annum for 5 years

   A.) Rs. 650
   B.) Rs. 550
   C.) Rs. 525
   D.) Rs. 615

Answer: Option 'A'

Given
Principal : 1300
Rate of interest : 10
Number of years : 5
Simple Interest = pnr / 100
Simple Interest = (1300 x 5 x 10) / 100
= 13 x 5 x 10
= 650 
So,Simple Interest = 650

9.

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

Answer: Option 'B'

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

10.

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%

Answer: Option 'A'

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

11.

What would be the compound interest accrued on an amount of 8000 Rs. at the end of 3 years at the rate of 10 % per annum ?

   A.) 10748
   B.) 2648
   C.) 1548
   D.) 10648

Answer: Option 'B'

Given
principal = 8000
No. of years = 3
Rate of interest = 10
Amount = P x ( 1 + ( r / 100 ) )n
= 8000 x ( 1 + ( 1 / 10 ) )3 
= 8000 x ( 11 / 10 )3 
= 8000 x ( 1331 / 1000 )
= 8 x 1331
Amount = 10648
Compound Interest = Amount - Principal
= 10648 - 8000
2648 Rs

12.

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

Answer: Option 'D'

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.

13.

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

Answer: Option 'B'

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.

14.

A person receives a sum of Rs. 420 as interest for investing some amount at 10% p.a compounding annually for 2 years. Find the amount invested at the beginning

   A.) 2050
   B.) 2000
   C.) 2100
   D.) 1900

Answer: Option 'B'

Given compound interest ( C.I ) = Rs.420
Rate of interest ( r ) = 10 %
Number of years ( n ) = 2
To find , amount invested at the beginning i.e principal (P)
Amount = P [ 1 + ( r / 100 ) ]n
Amount = C.I + P

=> Amount = C.I + P
=> P [ 1 + ( r / 100 ) ]n= C.I + P
=> P [ 1 + ( 10 / 100 ) ]2= 420 + P
=> P [ 110 / 100 ]2= 420 + P
=> P [ 11 / 10 ]2= 420 + P
=> P x 121 / 100 = 420 + P
=> ( 121 P / 100 ) - P = 420
=> ( 121 P - 100 P ) / 100 = 420
=> 21 P / 100 = 420
=> P = ( 420 * 100 ) / 21
= 2000 
Amount invested at the beginning, P = 2000 Rs

15.

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

Answer: Option 'B'

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.

16.

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

Answer: Option 'B'

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

17.

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

Answer: Option 'B'

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

18.

Find the simple interest on Rs. 2000 at 7 % per annum for 4 years

   A.)  Rs. 485
   B.)  Rs. 450
   C.)  Rs. 560
   D.)  Rs. 760

Answer: Option 'C'

Given
Principal : 2000
Rate of interest : 7
Number of years : 4
Simple Interest = pnr / 100 
= ( 2000 x 4 x 7 ) / 100
Rs. 560 

19.

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

Answer: Option 'B'

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

20.

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/-

Answer: Option 'C'

Rs.860/-


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