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Compound Interest Questions

61. A man gave 50% of his savings of Rs. 84,100 to his wife and divided the remaining sum among his two sons A and B of 15 and 13 years of age respectively. He divided it in such a way that each of his sons, when they attain the age of 18 years, would receive the same amount at 5% compound interest per annum. The share of B was




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Correct Ans:Rs. 20,000
Explanation:
Given, wife gets 50% of total savings of Rs. 84,100.
So, wife’s share = (50/100)*84100 = Rs. 42,050
Remaining sum = 84100 - 42050 = Rs. 42,050
Amount = P[1 + (R/100)]ⁿ

According to the question, A’s share = B’s share
A’s share[(1 + (5/100)]³ = B’s share[(1 + (5/100)]⁵
A’s share/B’s share = [(1 + (5/100)]⁵/[(1 + (5/100)]³
A’s share/B’s share = [(1 + (5/100)]⁵⁻³
A’s share/B’s share = (105/100)²
A’s share/B’s share = (21/20)²
Ratio of shares of A and B,
A’s share/B’s share = 441/400
B’s share = (Remaining sum/total ratio)*B’s ratio
= (42050/842)*400 = Rs.20,000
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62. A man borrows Rs. 12,500 at 20% compound interest. At the end of every year he pays Rs. 2000 as part of repayment. How much does he still owe after three such instalments?




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Correct Ans:Rs. 14,320
Explanation:
Principal = Rs. 12,500
Rate = 20% compounded per annum.
WKT, Amount = P[1+ (r/100)]n
Amount after first year = 12500*(120/100) = Rs. 15,000
Principal for second year = 15000 - 2000 = Rs. 13,000
Amount after second year = 13000*(120/100) = Rs. 15,600
Principal for third year = 15600 - 2000 = Rs. 13,600
Amount after third year = 13600*(120/100) = Rs. 16,320
Remaining amount = 16320 - 2000 = Rs. 14,320.
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63. Simple interest on a certain sum of money for 3 years at 5% per annum is half the compound interest on Rs 5000 for 2 years at 10% per annum. Find the principal amount on simple interest.




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Correct Ans:Rs. 3500
Explanation:
Let A be the amount obtained when Rs.5000 is compound annually.
WKT, CI = P(1 + (R/100))n - P
= 5000*(1 + (10/100))2 - 5000
= 5000*(110/100)2 - 5000
= 5000 * [(110*110)/(100*100)] - 5000
= 6050 - 5000
= Rs. 1050
Given, simple interest is half the compound interest = 1050/2 = Rs. 525
Let P be the sum of money invested on SI.
WKT, SI = PNR/100
525 = (P*5*3)/100
P = (525*100)/15
P = Rs. 3500
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64. Three persons Amar, Akbar and Anthony invested different amounts in a fixed deposit scheme for one year at the rate of 12% per annum and earned a total interest of Rs. 3,240 at the end of the year. If the amount invested by Akbar is Rs. 5000 more than the amount invested by Amar and the invested by Anthony is Rs. 2000 more than the amount invested by Akbar, what is the amount invested by Akbar ?
 




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Correct Ans:10,000
Explanation:
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65. Subash purchased a refrigerator on the terms that he is required to pay Rs.1,500 as cash down payment followed by Rs.1,020 at the end of first year, Rs.1,003 at the end of second year and Rs.990 at the end of third year. Interest is charged at the rate of 10% per annum. Calculate the cost price.




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Correct Ans:4000
Explanation:
Given
Cash Down Payment = Rs 1500
let X becomes 1020 at the end of 1st year

1020 = x ( 1 + (10 / 100) )
x = 1020 * 10 / 11
=> 927.27

It becomes 1003 at the end of 2nd year
y = 1003 * 20 * 20 * / 22 * 22
=> 828.92
It becomes 990 at the end of 3rd year
z= 990 * 10 * 10 * 10 / 11 * 11 * 11
=> 743.80
Cost Price =>1500 + 927.27 + 828.92 + 743.80
=> 3999.99 or 4000.
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66. Shawn invested one half of his savings in a bond that paid simple interest for 2 years and received Rs.550 as interest. He invested the remaining in a bond that paid compound interest, interest being compounded annually, for the same 2 years at the same rate of interest and received Rs.605 as interest. What was the value of his total savings before investing in these two bonds? 




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Correct Ans:Rs.2,750
Explanation:
Shawn received an extra amount of (Rs.605 – Rs.550) Rs.55 on his compound interest paying bond as the interest that he received in the first year also earned interest in the second year.

The extra interest earned on the compound interest bond = Rs.55
The interest for the first year =550/2 = Rs.275

Therefore, the rate of interest =55/275 * 100 = 20% p.a.

20% interest means that Shawn received 20% of the amount he invested in the bonds as interest.

If 20% of his investment in one of the bonds = Rs.275, then his total investment in each of the bonds = 275/20 * 100 = 1375.

As he invested equal sums in both the bonds, his total savings before investing = 2*1375 = Rs.2750
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67. Arun borrowed a certain sum from Manish at a certain rate of simple interest for 2 years. He lent this sum to Sunil at the same rate of interest compounded annually for the same period. At the end of two years, he received Rs. 2400 as compound interest but paid Rs. 2000 only as simple interest. Find the rate of interest. 




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Correct Ans:40%
Explanation:
Let the sum be x

Simple interest on x for 2 years = Rs.2000
Formula
Simple Interest = (P *R*T) / 100
2000 = x * R * 2 / 100
=> x R =100000 ---- (1)

Compound Interest on x for 2 years = 2400
P( 1 + R / 100 ) ^ T - P = 2400
=> x ( 1+ R / 100 ) ^ 2 - x = 2400
=> x ( 1 + 2R / 100 + R ^ 2 / 10000)- x = 2400
=> x ( 2R / 100 + R ^ 2 /10000 ) = 2400
=> 2 x R / 100 +x R ^ 2 /10000 ) = 2400 -----(2)

Substituting the value of xR from (1) in (2) ,we get
=> 2 * (100000 / 100) +100000 * (R /10000) = 2400
=>2000 + 10 R = 2400
=> 10 R = 2400 - 2000
=> 10 R = 400
=> R = 400 / 10
=> R = 40 %.
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68. 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? 




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Correct Ans:3 years
Explanation:
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.
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69. 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. 




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Correct Ans:Rs. 8,000
Explanation:
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
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70. 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? 




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Correct Ans:Rs.14,04,816
Explanation:
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
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71. 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.




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Correct Ans:1000
Explanation:
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
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72. 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?




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Correct Ans:4137.5
Explanation:
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
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73. 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.  




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Correct Ans:22472
Explanation:
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
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74. 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 ?




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Correct Ans:10816
Explanation:
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
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75. Find the simple interest on Rs. 2000 at 7 % per annum for 4 years




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Correct Ans:560 Rs.
Explanation:
Solution is :
Given

Principal : 2000
Rate of interest : 7
Number of years : 4
Simple Interest = pnr / 100
= ( 2000 x 4 x 7 ) / 100
=560 Rs
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76. 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? 




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Correct Ans:816
Explanation:
Given: Principal = Rs.10,000
n = 2
r = 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
= Rs.10,816
Compound Interest = Amount - Principal

= 10816 - 10000
= Rs. 816
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77. 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




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Correct Ans:10000
Explanation:

Solution is :
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

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78. 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 ?




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Correct Ans:2096.25
Explanation:
Solution is :
Given principal = 6500
No. of years = 2
Rate of interest = 15
Amount = P [ 1 + ( r / 100 )n]
= 6500 x [ 1 + ( 15 /100 )2]
= 6500 x [ 1 + ( 3 / 20 )2]
= 6500 x [ 23 / 20 ]2
= 6500 x [ 529 / 400 ]
Amount =8596.25
Compound Interest = Amount - Principal

= 8596.25 - 6500
= 2096.25
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79. 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 ?




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Correct Ans:945
Explanation:
Solution is :
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
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80. 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. 




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Correct Ans:10,000
Explanation:
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.
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