1.
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.
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
2.
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.
Answer: Option 'B'
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
3.
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.
Answer: Option 'A'
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.
4.
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
Answer: Option 'B'
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
5.
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?
Answer: Option 'A'
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
6.
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?
Answer: Option 'A'
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
7.
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?
Answer: Option 'A'
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
8.
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 ?
Answer: Option 'A'
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
9.
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
Answer: Option 'C'
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
10.
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 ?
Answer: Option 'A'
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
= Rs 2648
11.
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?
Answer: Option 'B'
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.
12.
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?
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.
13.
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?
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.
14.
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?
Answer: Option 'A'
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
15.
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.
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.
16.
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 ?
Answer: Option 'B'
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
17.
Find the simple interest on Rs. 2000 at 7 % per annum for 4 years
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
18.
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 ?
Answer: Option 'A'
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
19.
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 ?
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
20.
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?
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