Ex.1. Find
compound interest on Rs.
7500 at
4% per annum for 2 years,
compounded annually.
Sol. Amount = Rs [7500*(1+(4/100)2] = Rs (7500 * (26/25) * (26/25)) = Rs. 8112.
Therefore, C.I. = Rs. (8112 - 7500) = Rs. 612.
Ex. 2. Find compound interest on Rs. 8000 at 15% per annum for 2 years 4 months, compounded annually.
Sol. Time = 2 years 4 months = 2(4/12) years = 2(1/3) years.
Amount = Rs'. [8000 X (1+(15/100))2 X (1+((1/3)*15)/100)]
=Rs. [8000 * (23/20) * (23/20) * (21/20)] = Rs. 11109. .
:. C.I. = Rs. (11109 - 8000) = Rs. 3109.
Ex. 3. Find the compound interest on Rs. 10,000 in 2 years at 4% per annum, the interest being compounded half-yearly
Sol. Principal = Rs. 10000; Rate = 2% per half-year; Time = 2 years = 4 half-years.
Amount = Rs [10000 * (1+(2/100))4] = Rs(10000 * (51/50) * (51/50) * (51/50) * (51/50))
Sol. Amount = Rs [7500*(1+(4/100)2] = Rs (7500 * (26/25) * (26/25)) = Rs. 8112.
Therefore, C.I. = Rs. (8112 - 7500) = Rs. 612.
Ex. 2. Find compound interest on Rs. 8000 at 15% per annum for 2 years 4 months, compounded annually.
Sol. Time = 2 years 4 months = 2(4/12) years = 2(1/3) years.
Amount = Rs'. [8000 X (1+(15/100))2 X (1+((1/3)*15)/100)]
=Rs. [8000 * (23/20) * (23/20) * (21/20)] = Rs. 11109. .
:. C.I. = Rs. (11109 - 8000) = Rs. 3109.
Ex. 3. Find the compound interest on Rs. 10,000 in 2 years at 4% per annum, the interest being compounded half-yearly
Sol. Principal = Rs. 10000; Rate = 2% per half-year; Time = 2 years = 4 half-years.
Amount = Rs [10000 * (1+(2/100))4] = Rs(10000 * (51/50) * (51/50) * (51/50) * (51/50))
= Rs. 10824.32.
:. C.I. = Rs. (10824.32 - 10000) = Rs. 824.32.
:. C.I. = Rs. (10824.32 - 10000) = Rs. 824.32.
Ex.
4. Find
the compound interest on Rs.
16,000 at 20%
per annum for 9 months, compounded
quarterly.
Sol. Principal = Rs. 16000; Time = 9 months =3 quarters;
Rate = 20% per annum = 5% per quarter.
Amount = Rs. [16000 x (1+(5/100))3] = Rs. 18522.
CJ. = Rs. (18522 - 16000) = Rs. 2522.
Ex. 5. If the simple interest on a sum of money at 5% per annum for 3 years is Rs. 1200, find the compound interest on the same sum for the same period at the same rate.
Sol. Clearly, Rate = 5% p.a., Time = 3 years, S.I.= Rs. 1200. . .
So principal=RS [100*1200]/3*5=RS 8000
Amount = Rs. 8000 x [1 +5/100]^3 - = Rs. 9261.
.. C.I. = Rs. (9261 - 8000) = Rs. 1261.
Ex. 6. In what time will Rs. 1000 become Rs. 1331 at 10% per annum compounded annually?
Sol. Principal = Rs. 1000; Amount = Rs. 1331; Rate = 10% p.a. Let the time be n years. Then,
[ 1000 (1+ (10/100))n ] = 1331 or (11/10)n = (1331/1000) = (11/10)3 n = 3 years.
Ex. 7. If Rs. 600 amounts to Rs. 683.20 in two years compounded annually, find the rate of interest per annum.
Sol. Principal = Rs. 500; Amount = Rs. 583.20; Time = 2 years.
Let the rate be R% per annum.. 'Then,
[ 500 (1+(R/100)2 ] = 583.20 or [ 1+ (R/100)]2 = 5832/5000 = 11664/10000
[ 1+ (R/100)]2 = (108/100)2 or 1 + (R/100) = 108/100 or R = 8
So, rate = 8% p.a.
Ex. 8. If the compound interest on a certain sum at 16 (2/3)% to 3 years is Rs.1270, find the simple interest on the same sum at the same rate and f or the same period.
Sol. Let the sum be Rs. x. Then,
C.I. = [ x * (1 + (( 50/(3*100))3- x ] = ((343x / 216) - x) = 127x / 216
127x /216 = 1270 or x = (1270 * 216) / 127 = 2160.
Thus, the sum is Rs. 2160
S.I. = Rs ( 2160 * (50/3) * 3 * (1 /100 ) ) = Rs. 1080.
Ex. 9. The difference between the compound interest and simple interest on a certain sum at 10% per annum for 2 years is Rs. 631. Find the sum.
Sol. Let the sum be Rs. x. Then,
C.I. = x ( 1 + ( 10 /100 ))2 - x = 21x / 100 ,
S.I. = (( x * 10 * 2) / 100) = x / 5
(C.I) - (S.I) = ((21x / 100 ) - (x / 5 )) = x / 100
( x / 100 ) = 632 ó x = 63100.
Hence, the sum is Rs.63,100.
Ex. 10. The difference between the compound interest and the simple interest accrued on an amount of Rs. 18,000 in 2 years was Rs. 405. What was the rate of interest p.c.p.a. ?
Sol. Let the rate be R% p.a. then,
[ 18000 ( 1 + ( R / 100 )2 ) - 18000 ] - ((18000 * R * 2) / 100 ) = 405
18000 [ ( 100 + (R / 100 )2 / 10000) - 1 - (2R / 100 ) ] = 405
18000[( (100 + R ) 2 - 10000 - 200R) / 10000 ] = 405
9R2 / 5 = 405 R2ó =((405 * 5 ) / 9) = 225 R = 15. Rate = 15%.
Ex. 11. Divide Rs. 1301 between A and B, so that the amount of A after 7 years is equal to the amount of B after 9 years, the interest being compounded at 4% per annum.
Sol. Let the two parts be Rs. x and Rs. (1301 - x).
x(1+4/100)7 =(1301-x)(1+4/100)9
x/(1301-x)=(1+4/100)2=(26/25*26/25)
625x=676(1301-x)
1301x=676*1301
x=676.
So,the parts are rs.676 and rs.(1301-676)i.e rs.676 and rs.625.
Ex.12. a certain sum amounts to rs.7350 in 2 years and to rs.8575 in 3 years.find the sum and rate percent.
S.I on rs.7350 for 1 year=rs.(8575-7350)=rs.1225.
Rate=(100*1225/7350*1)%=16 2/3%
Let the sum be rs.x.then,
X(1+50/3*100)2=7350
X*7/6*7/6=7350
X=(7350*36/49)=5400.
Sum=rs.5400.
Ex.13.a sum of money amounts to rs.6690 after 3 years and to rs.10,035 after 6 years on compound interest.find the sum.
Sol. Let the sum be rs.P.then
P(1+R/100)3=6690…(i) and P(1+R/100)6=10035…(ii)
On dividing,we get (1+R/100)3=10025/6690=3/2.
Substituting this value in (i),we get:
P*3/2=6690 or P=(6690*2/3)=4460
Hence,the sum is rs.4460.
Sol. Principal = Rs. 16000; Time = 9 months =3 quarters;
Rate = 20% per annum = 5% per quarter.
Amount = Rs. [16000 x (1+(5/100))3] = Rs. 18522.
CJ. = Rs. (18522 - 16000) = Rs. 2522.
Ex. 5. If the simple interest on a sum of money at 5% per annum for 3 years is Rs. 1200, find the compound interest on the same sum for the same period at the same rate.
Sol. Clearly, Rate = 5% p.a., Time = 3 years, S.I.= Rs. 1200. . .
So principal=RS [100*1200]/3*5=RS 8000
Amount = Rs. 8000 x [1 +5/100]^3 - = Rs. 9261.
.. C.I. = Rs. (9261 - 8000) = Rs. 1261.
Ex. 6. In what time will Rs. 1000 become Rs. 1331 at 10% per annum compounded annually?
Sol. Principal = Rs. 1000; Amount = Rs. 1331; Rate = 10% p.a. Let the time be n years. Then,
[ 1000 (1+ (10/100))n ] = 1331 or (11/10)n = (1331/1000) = (11/10)3 n = 3 years.
Ex. 7. If Rs. 600 amounts to Rs. 683.20 in two years compounded annually, find the rate of interest per annum.
Sol. Principal = Rs. 500; Amount = Rs. 583.20; Time = 2 years.
Let the rate be R% per annum.. 'Then,
[ 500 (1+(R/100)2 ] = 583.20 or [ 1+ (R/100)]2 = 5832/5000 = 11664/10000
[ 1+ (R/100)]2 = (108/100)2 or 1 + (R/100) = 108/100 or R = 8
So, rate = 8% p.a.
Ex. 8. If the compound interest on a certain sum at 16 (2/3)% to 3 years is Rs.1270, find the simple interest on the same sum at the same rate and f or the same period.
Sol. Let the sum be Rs. x. Then,
C.I. = [ x * (1 + (( 50/(3*100))3- x ] = ((343x / 216) - x) = 127x / 216
127x /216 = 1270 or x = (1270 * 216) / 127 = 2160.
Thus, the sum is Rs. 2160
S.I. = Rs ( 2160 * (50/3) * 3 * (1 /100 ) ) = Rs. 1080.
Ex. 9. The difference between the compound interest and simple interest on a certain sum at 10% per annum for 2 years is Rs. 631. Find the sum.
Sol. Let the sum be Rs. x. Then,
C.I. = x ( 1 + ( 10 /100 ))2 - x = 21x / 100 ,
S.I. = (( x * 10 * 2) / 100) = x / 5
(C.I) - (S.I) = ((21x / 100 ) - (x / 5 )) = x / 100
( x / 100 ) = 632 ó x = 63100.
Hence, the sum is Rs.63,100.
Ex. 10. The difference between the compound interest and the simple interest accrued on an amount of Rs. 18,000 in 2 years was Rs. 405. What was the rate of interest p.c.p.a. ?
Sol. Let the rate be R% p.a. then,
[ 18000 ( 1 + ( R / 100 )2 ) - 18000 ] - ((18000 * R * 2) / 100 ) = 405
18000 [ ( 100 + (R / 100 )2 / 10000) - 1 - (2R / 100 ) ] = 405
18000[( (100 + R ) 2 - 10000 - 200R) / 10000 ] = 405
9R2 / 5 = 405 R2ó =((405 * 5 ) / 9) = 225 R = 15. Rate = 15%.
Ex. 11. Divide Rs. 1301 between A and B, so that the amount of A after 7 years is equal to the amount of B after 9 years, the interest being compounded at 4% per annum.
Sol. Let the two parts be Rs. x and Rs. (1301 - x).
x(1+4/100)7 =(1301-x)(1+4/100)9
x/(1301-x)=(1+4/100)2=(26/25*26/25)
625x=676(1301-x)
1301x=676*1301
x=676.
So,the parts are rs.676 and rs.(1301-676)i.e rs.676 and rs.625.
Ex.12. a certain sum amounts to rs.7350 in 2 years and to rs.8575 in 3 years.find the sum and rate percent.
S.I on rs.7350 for 1 year=rs.(8575-7350)=rs.1225.
Rate=(100*1225/7350*1)%=16 2/3%
Let the sum be rs.x.then,
X(1+50/3*100)2=7350
X*7/6*7/6=7350
X=(7350*36/49)=5400.
Sum=rs.5400.
Ex.13.a sum of money amounts to rs.6690 after 3 years and to rs.10,035 after 6 years on compound interest.find the sum.
Sol. Let the sum be rs.P.then
P(1+R/100)3=6690…(i) and P(1+R/100)6=10035…(ii)
On dividing,we get (1+R/100)3=10025/6690=3/2.
Substituting this value in (i),we get:
P*3/2=6690 or P=(6690*2/3)=4460
Hence,the sum is rs.4460.
Ex.14. a sum of money doubles itself at compound
interest in 15 years.in how many years will it beco,e eight times?
P(1+R/100)15=2P
(1+R/100)15=2P/P=2
LET P(1+R/100)n=8P
(1+R/100)n=8=23={(1+R/100)15}3[USING (I)]
(1+R/100)N=(1+R/100)45
n=45.
Thus,the required time=45 years.
P(1+R/100)15=2P
(1+R/100)15=2P/P=2
LET P(1+R/100)n=8P
(1+R/100)n=8=23={(1+R/100)15}3[USING (I)]
(1+R/100)N=(1+R/100)45
n=45.
Thus,the required time=45 years.
Ex.15.What annual payment will
discharge a debt of Rs.7620 due in 3years at 16and
2/3% per annum interest?
Sol. Let each installment beRs.x.
Then,(P.W. of Rs.x due 1 year hence)+(P>W of Rs.x due 2 years hence)+(P.W of Rs. X due 3
years hence)=7620.\ x/(1+(50/3*100))+ x/(1+(50/3*100))2 + x/(1+(50/3*100))3=7620
(6x/7)+(936x/49)+(216x/343)=7620.
294x+252x+216x=7620*343.
x=(7620*343/762)=3430.
Amount of each installment=Rs.3430.
Sol. Let each installment beRs.x.
Then,(P.W. of Rs.x due 1 year hence)+(P>W of Rs.x due 2 years hence)+(P.W of Rs. X due 3
years hence)=7620.\ x/(1+(50/3*100))+ x/(1+(50/3*100))2 + x/(1+(50/3*100))3=7620
(6x/7)+(936x/49)+(216x/343)=7620.
294x+252x+216x=7620*343.
x=(7620*343/762)=3430.
Amount of each installment=Rs.3430.
This is very beneficial for finance students… Understanding Compound Interest term is very important and this has helped a lot.
ReplyDeletewhat a great exercise
ReplyDeletestill improve but thanks
ReplyDeleteThank u very much
ReplyDeleteQuestions are good but the solutions are not given clearly... Can't understand the solutions and question 7 is given wrong so its needs to be corrected and improved...
ReplyDeleteBut thanks .. These questions helped
Can someone please solve this question for me?
ReplyDeleteMahesh borrowed a certain sum of money for 2 years simple interest from Bhim. Mahesh lent this sum to Vishnu at 2 years compound interest. After 2 years, Mahesh received Rs. 410 compound interest but paid Rs.400 simple interest to Bhim. Find the sum and rate of interest.
NYC.... Helped me somewhat.... Gud questions
DeleteP=4000 ans
DeleteRate=5% p=4000 ans
DeleteRate=5% p=4000 ans
DeleteRate is 5%
DeletePrinciple is ₹4000
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ReplyDeleteExcellent questions. Thanks
ReplyDeleteThese all questions are solved problems of quantitative aptitude book S.chand.. Plz go for originality not copy paste
ReplyDeletevery true
DeleteFind the compound interest at the rate of 10% per annum for four year on the principal which in 4 years at the rate of 4% per annum gives Rs.1600 as simple interest?
ReplyDeleteThis comment has been removed by the author.
ReplyDeletePlz solve on what sum will the compound interest at 7.5% per annum for three years compounded annually be ₹3,101.40.
ReplyDeleteThank you for the information. Here are some useful information for board exam class 10th and 12th
ReplyDeleteCBSE Class 10th Sample Papers
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CBSE Class 12th Sample Papers
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