1. The difference between compound interest and simple interest on a sum for 2 yrs at 20% per annum, when the interest is compounded annually is Rs 240. If the interest were compounded half yearly, the difference in two interests over same period would be ?
A. Rs 384.6
B. Rs 344.2
C. Rs 324.8
D. Rs 316.5
E. None of these
Sol. Difference for 2 yrs = P*20*20/100*100 = 240
Solving, we get,
P = 6000
So SI for 2 yrs = 6000*20*2/100 = 2400
Amount at compounded half yearly = 6000 [1 + 10/100]^4
Solving,we get,
Amount at compounded half yearly = 8784.6
So CI at compounded half yearly = 8784.6 – 6000 = 2784.6
So difference = 2784.6 – 2400 = Rs 384.6
2. X borrows a sum of Rs.100,000 from a bank @ 10% p.a. compounded annually for 2 years. He then lends Rs.20,000, compounded every 8 months @ 10%, to each of his five friends for a period of two years. At the end of two years, X collects all the money from his friends and clears his debt with the bank. How much money did X make at the end of the two-year period ?
A. 12,100
B. 14,100
C. 15,100
D. 4,971
E. 13,200
Sol. The amount to be paid to bank after 2 years will be 100000 × (1.1)2 = Rs.121,000.
A 2-year period will be made up of three 8-month periods, each of which will cost each of the friends 10%.
The amount that each of the friends will pay back after 2 years will be 20000 × (1.1)3 = Rs.26620.
So, the total sum of money collected from the five friends will be 5 × 26620 = Rs.133,100.
After clearing his debt with the bank, X will have made 133100 – 121000 = Rs.12,100.
3. X lent Rs 2500 to Y for 4 years and Rs 4000 to Z for 3 years on simple interest at the same rate of interest and received Rs 4400 in all from both of them as interest. The rate of interest per annum is:
A. 25%
B. 17%
C. 22%
D. 20%
E. None of these
Sol. Let the rate of interes be R%. Then,
(2500*R*4)/100 + (4000*R*3)/100 = 4400
R = 4400/220 = 20%.
4. The simple interest on a sum of money is 8/25 of sum. If the number of years numerically is half the rate of interest then what is the rate of interest ?
A. 5
B. 4
C. 6
D. 8
E. None of these
Sol. Given, S.I. = (8/25)P
Time = t = R/2
Now, S.I.= PRT/100
(8/25)P = [P*R*(R/2)]/100
Solving, R = 6%.
5. What sum of money will amount to Rs. 520 in 5 years and to Rs. 568 in 7 years at simple interest?
A. Rs. 400
B. Rs. 120
C. Rs. 510
D. Rs. 220
E. None of these
Sol. Rate % = 100(568 - 520)/[520*7 - 568*5] = 6%
Sum = (568 - 520)*100/[(7-5)*6] = Rs 400.
6. Deepak borrows Rs.5000 at simple Interest from a lender. At the end of 3 years, she again borrows Rs.2000 and settled that amount after paying Rs.5000 as interest after 8 years from the time she made the first borrowing. what is the rate of interest ?
A. 5%
B. 7%
C. 9%
D. 10%
E. None of these
Sol. SI for Rs.5000 for 8 years= (5000*r*8)/100
Again borrowed=2000
SI = (2000*r*5)/100
Total interest= [(5000*r*8)/100] + [(2000*r*5)/100] = 5000
400r + 100r = 5000
r = 10%
7. A sum was put at simple interest at certain rate for 3 years. Had it been put at 5% higher rate, it would have fetched Rs 108 more. What is the sum ?
A. 360
B. 480
C. 720
D. 960
E. None of these
Sol. Let the sum be S.
108 = S*5*3/100
S = Rs 720.
8. The ratio of amount for two years under CI per annum and for one year under SI is 4/3, when the rate of interest is same, Find the rate of Interest ?
A. 100/3 %
B. 25 %
C. 33/2 %
D. None of these
E. Can't be determined
Sol. SI for 1 year = CI for 1 year
P(1+r/100)2 /P(1+r/100) = 4/3
1+ r/100 = 4/3
r/100 = 4/3 -1 = 1/3
r = 100/3 %
9. There are 2 schemes A and B, both have 12% interest rate. A person invests in them in the ratio of 3:4. After 3 years, the difference between interest from A and interest from B is Rs 360, calculate the amount invested in scheme A ?
A. 4000
B. 3000
C. 2000
D. 1000
E. None of these
Sol. Lets assume investment by A to be '3x'.
Assume invested by B to be '4x'.
S.I. from A = (3x*3*12)/100 = 1.08x
S.I. from B = (4x*3*12)/100 = 1.44x
Difference = 1.44x - 1.08x = 0.36x
Thus, 0.36x = 360
x = Rs 1000
Investment by A = 3*1000 = Rs 3000.
10. A sum of money doubles itself in 8 years at simple interest . In how many years will it triple?
(a) 16 years
(b) 15 years
(c) 14 years
(d) 12 years
(e) None of these
Sol. P = P*R*8/100
R = 100/8
Thus, 2P = (P*T*100)/(8*100)
T = 16 yrs.
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