Q.1
Find compound interest on Rs. 7500 at 4% per annum for 2 years, compounded annually.
612
620
650
510
Ans .
612
- Explanation :
Amount = Rs [7500*\((1+(4/100)^2\)] = Rs (7500 * (26/25) * (26/25)) = Rs. 8112.
therefore, C.I. = Rs. (8112 - 7500) = Rs. 612.
Q.2
Find compound interest on Rs. 8000 at 15% per annum for 2 years 4 months, compounded annually.
2000
2109
3109
3000
Ans .
3109
- Explanation :
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.
Q.3
Find the compound interest on Rs. 10,000 in 2 years at 4% per annum, the interest being compounded half-yearly
830
825.32
825
824.32
Ans .
824.32
- Explanation :
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.
Q.4
Find the compound interest on Rs. 16,000 at 20% per annum for 9 months,compounded quarterly
2000
2522
3522
3500
Ans .
2522
- Explanation :
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
Q.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.
1261
1360
1260
1161
Ans .
1261
- Explanation :
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.
Q.6 In what time will Rs. 1000 become Rs. 1331 at 10% per annum compounded annually?
2 ys
3 yrs
4 yrs
2 yrs 5 months
Ans .
3 yrs
- Explanation :
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.
Q.7
If Rs. 600 amounts to Rs. 683.20 in two years compounded annually, find the rate of interest per annum.
8% p.a.
10% p.a.
5% p.a.
7% p.a.
Ans .
8% p.a.
- Explanation
:
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.
Q.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.
1080
1050
1110
2050
Ans .
1080
- Explanation :
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.
Q.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.
Rs.53,110.
Rs.63,100.
Rs.60,000.
Rs.73,100.
Ans .
Rs.63,100.
- Explanation
:
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
Hence, the sum is Rs.63,100.
Q.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. ?
7%.
11%.
13%.
15%.
Ans .
15%.
- Explanation :
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 9\(R^2\) / 5 = 405 \(R^2\) =((405 * 5 ) / 9) = 225
R = 15. Rate = 15%.
Q.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.
Rs.676 and rs.665.
Rs.676 and Rs.625.
Rs.776 and Rs.725.
Rs.576 and Rs.625.
Ans .
Rs.676 and Rs.625.
- Explanation :
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.
Q.12
a certain sum amounts to rs.7350 in 2 years and to rs.8575 in 3 years.find the sum and rate percent.
Rs.5200
Rs.5000
Rs.4400
Rs.5400
Ans .
Rs.5400
- Explanation :
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
Q.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.
Rs.4460.
Rs.4660.
Rs.5560.
Rs.3460.
Ans .
Rs.4460.
- Explanation :
. 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.
Q.14
a sum of money doubles itself at compound interest in 15 years.in how many years will it beco,e eight times?
55 years
25 years
35 years
45 years
Ans .
45 years
- Explanation :
\(P(1+R/100)^15\)=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
Q.15
What annual payment will discharge a debt of Rs.7620 due in 3years at 16 2/3% per annum interest?
Rs.4430
Rs.3550
Rs.3430
Rs.5430
Ans .
Rs.3430
- Explanation :
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 3years 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.