1. 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.
2. Akarsh left a will of Rs. 16,400 for his two sons aged 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
3. 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
4. A bank offers 5% compound interest calculated on half-yearly basis. A customer deposits Rs. 1600 each on 1st January and 1st July of a year. At the end of the year, the amount he would have gained by way of interest?
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Correct Ans:121
Explanation:
Given to find out the compound interest at half yearly basis
Step 1:
Amount after 1 year on Rs. 1600 (deposited on 1st Jan) at 5% when interest calculated half-yearly
=> P (1+(R/2)/100)^2T
Here, Principal (P) = Rs. 1600
R = 5%
T = 1 year
By substituting we get
=> 1600(1+(5/2) /100) ^ 2*1
=> 1600 [1+( 1/ 40)] ^ 2
Step 2:
Amount after 1/2 year (ie., 6 months) on Rs. 1600 (deposited on 1st July) at 5% when interest calculated half-yearly
=> P(1+(R/2)/100)^2T
Here, Principal (P) = Rs. 1600
R = 5%
T = 1/2 year
=> 1600[ 1+(5/2 ) / 100] ^ (2 * 1/2)
=>1600 [1+ (1/40)]
Step 3:
Total Amount after 1 year
=1600 [1+(1/ 40) ^ 2] + 1600 [1+(1/40)]
= 1600 [41 / 40] ^ 2] + 1600 [41 / 40]
=1600 (41 / 40) * [(41 / 40) + 1]
=1600(41/ 40)* (81/ 40)
= 41 * 81
= Rs. 3321
Step 4:
To find compound interest
Compound interest = Compound Amount - Principal
=> Principal (for two half year) = 1600 + 1600 =3200
=>Compound interest = 3321- 3200
=Rs. 121
5. 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
6. 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:
Principal : P = 20,000 Rs.
Rate of Interest : r = 6 %
Number of years : n = 2
Amount = P x (1 + r/100)^{n}
=> Amount = 20,000 x (1+6/100)^{2}
=20000 x (1+3/50)^{2}
=20000 x (53/50) x (53/50)
=561800 / 25
= 22472
Thus, the Amount that John receives at the end of 2 years= Rs.22472
7. 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
8. 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 ?
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Correct Ans:2206.75
Explanation:
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 (1 + 1/20)^3
= 14000 x (21/20)^3
= 14000 x (21/20) x (21/20) x (21/20)
= 16206.75
Compound Interest = Amount - Principal
= 16206.75 - 14000
= 2206.75.
9. 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
10. 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
11. 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
12. 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 = 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
13. 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
14. 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
15. 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
16. 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 ?
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Correct Ans:2648
Explanation:
Solution is
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
&nb
17. Find the simple interest on Rs. 1920 at 45 % per annum for 3 months
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Correct Ans:Rs. 216
Explanation:
Solution is:
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
18. 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
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Correct Ans:2000
Explanation:
Solution is
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
19. Find the simple interest on Rs. 1300 at 10 % per annum for 5 years
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Correct Ans:Rs. 650
Explanation:
Solution is
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
20. 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
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Correct Ans:1000
Explanation:
Solution is
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 = 1000 Rs
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