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Compound Interest Questions

41. Sum invested in scheme A, which offers compound interest (compounded annually) at 10% pa, is 50% of that in scheme B, which offers compound interest (compounded annually) at 20% pa. The duration of investment in each of the schemes is 2 years. If the difference between the amounts received from schemes A and B is Rs. 3507, what is the sum invested in scheme B? (in rupees)




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Correct Ans:Rs. 4200
Explanation:
Let the investment in scheme B be Rs. x.
Investment in scheme A = Rs. x/2
According to the question,
A = P(1 + (R/100))T
x(1 + (20/100))2 - x/2(1 + (10/100))2 = 3507
x(6/5)2 - x/2(11/10)2 = 3507
36x/25 - 121x/200 = 3507
(288x - 121x)/200 = 3507
167x = 3507*200
x = (3507*200)/167
= Rs. 4200
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42. Raman invested Rs. P for 2 years in scheme A which offered 20% per annum compound interest (compound annually). He lent the interest earned from scheme A to Shubh, at the rate of 7.5% per annum simple interest. If at the end of 2 years, Subh gave Rs. 3036 to Raman and thereby repaid the whole amount (actual loan + interest), what is the value of P ?




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Correct Ans:Rs. 6000
Explanation:
CI = P[(1 + R/100)T - 1]
= P[(1 + 20/100)2 - 1]
= P[(6/5)2 - 1]
= P[(36/25) - 1] = Rs. 11P/25
SI = PTR / 100
= (11P/25) * (2*7.5/100)
= Rs. 33P/500
According to the question,
33P/500 + 11P/25 = 3036
(33P + 220P)/500 = 3036
253P = 3036*500
P = (3036*500)/253 = Rs. 6000
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43. The compound interest (Compounded annually) on Rs. 9300 for 2 years at the rate of R% p.a. is Rs. 4092. Had the rate of interest been (R-10)%, what would have been the interest on the same sum of money for the same time ? (2 years) 




SHOW ANSWER
Correct Ans:Rs. 1953
Explanation:
Amount = Rs. (9300 + 4092) = Rs. 13392
A = P(1 + R/100)T
13392 = 9300(1 + R/100)2
13392/9300 = (1 + R/100)2
144/100 = (1 + R/100)2
(12/10)2 = (1 + R/100)2
12/10 = (1 + R/100)
R/100 = 12/10 - 1 = 2/10
R = (2/10)*100 = 20% p.a.
New rate = (R - 10)% = 10%
CI = P[(1 + R/100)T - 1]
= 9300[(1 + 10/100)2 - 1]
= 9300[(11/10)2 - 1]
= 9300(121/100 - 1)
= (9300*21)/100
CI = Rs. 1953
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44. The simple interest on a sum is Rs.1600 when the rate of interest is taken as 6% per year and the time is 4 years. Find the compound interest on the same amount of money.




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Correct Ans:Rs.1,750
Explanation:
Simple Interest (S.I.) = Rs.1600
Time(T) = 4 Years
Rate of Interest (R) = 6% per year
To find Principal,
Formula to calculate Simple Interest:
SI = PRT/100
SI= Simple Interest; P=Principal
S.I. = (PRT)/100
1600 = (P*6*4)/100
1600*100 = P*24
(1600*100)/24 = P
P = Rs.6,667
Therefore, the sum of money is Rs.6,667.
To find compound interest (C.I.) for the same sum,
Formula for Compound Interest (C.I)
C.I. = [P*(1+R/100)N] – P
C.I. = [6667*(1+6/100)4] – 6667
C.I. = Rs. 1,750
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45. A certain sum of money amounts to Rs. 2,420 in 2 years and Rs. 2,662 in 3 years at same rate of compound interest, compounded annually. The rate of interest per annum is: 




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Correct Ans:10%
Explanation:
Given:
Sum of money amounts in 2 yrs = Rs. 2420
Sum of money amounts in 3 yrs = Rs. 2662
So, interest on Rs.2420 for 1 yr = 2662 - 2420
= Rs. 242
SI = PNR/100
242 = (2420 x 1 x R)/100
R = (242 x 100)/2420
R = 10%.
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46. A sum of money is accumulating at compound interest at a certain rate of interest. If simple interest instead of compound were reckoned, the interest for the first two years would be diminished by Rs. 20 and that for the first three years by Rs. 61. Find the sum. 




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Correct Ans:Rs. 8000
Explanation:
Given:
Difference between CI and SI for 2 yrs = 20
PR²/100² = 20 ...(1)
Also given,
Difference between CI and SI for 3 yrs = 61
PR²/100²[(300 + R)/100] = 61
20[(300 + R)/100] = 61
300 + R = (61/20)*100
300 + R = 305
R = 5%

From (1),
P = 20*(100²/5²)
P = Rs. 8000
Therefore, sum is Rs.8000.
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47. The compound interest on a sum of money for 2 years is Rs. 832 and the simple interest on the same sum for the same period is Rs. 800. The difference between the compound interest and the simple interest for 3 years at the same rate will be: 




SHOW ANSWER
Correct Ans:Rs. 98.56
Explanation:
Given: N = 2 yrs; CI = Rs.832; SI = Rs.800
Difference between CI and SI for 2 yrs = 832 - 800
PR²/100² = 832 - 800
PR²/100² = 32 .......(1)

SI for 2 yrs = Rs.800
PNR/100 = 800
2PR/100 = 800 ....(2)
Divide (1) by (2),
R/200 = 32/800
R = 8%

Therefore, Principal = SI x(100/NR)
Principal = (800 x 100)/(2 x 8)
Principal = Rs. 5000
Difference between CI and SI for 3 yrs = PR²(300 + R)/100³
= (5000 x 8² x (300 + 8))/100³
= Rs. 98.56
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48. Shilpa took a loan of Rs. 15,00,000 to purchase a car. The company charges compound interest at 20% per annum. She promised to make the payment after three years. But for the last year of loan tenure, the company increased the rate of interest by 25% from the previous one. Then the extra amount which she had to pay is what per cent of the amount of loan taken by her? 




SHOW ANSWER
Correct Ans:7.20%
Explanation:
Given: P = Rs. 15,00,000
Rate of interest for 2 yrs = 20%
Rate of interest for last one yr = 125% of 20
= (125/100)*20 = 25%
WKT, A = P[1 + (r/100)]n
According to the question,
= 15,00,000{[1 + (20/100)]2[1 + (25/100)1]} - 15,00,000[1 + (20/100)]3
= 15,00,000{[1.2]2[1.25]} - 15,00,000[1.2]3
= 15,00,000(1.8 - 1.728)
= 15,00,000 x 0.072
= Rs.1,08,000

Required percentage = (108000/1500000)*100 = 7.20%.
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49. Rs. 2,60,200 is divided between Ram and Shyam so that the amount that Ram receives in 4 years is the same as that Shyam receives in 6 years. If the interest is compounded annually at the rate of 4% per annum then Ram’s share is




SHOW ANSWER
Correct Ans:Rs. 1,35,200
Explanation:
Let Ram's share be 'Rs. x'.
Therefore, Shyam share = Rs. (260200 - x)
WKT, A = P[1 + (R/100)]n

According to the question,amount recieved by Ram is same as that of Shyam,
x[1 + (4/100)]4 = (260200 - x)[1 + (4/100)]6
x = (260200 - x)[1 + (4/100)]2
x = (260200 - x)[1 + (1/25)]2
x = (260200 - x)[26/25]2
x = (260200 - x) (676/625)
(625x/676) = 260200 - x
(625x/676) + x = 260200
(625x + 676x)/676 = 260200
1301x = 260200*676
x = (260200*676)/1301
x = Rs. 1,35,200

Therefore, Ram's share is Rs. 1,35,200.
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50. Lata had Rs. 40,000. She invested some amount in scheme A at CI at 15% and the remaining amount in scheme B at SI at 10%. If she got the same interest from both the investments at the end of one year. How much rupees did she invest in scheme B? 




SHOW ANSWER
Correct Ans:Rs. 24,000
Explanation:
Let the amount invested in the scheme A be 'Rs. X'.
Therefore, the amount invested in the scheme B = (40000 - X).

Given that the simple and compound interest for 1st year is same.
According to the question,
15% of X = 10% of (40000 - X)
15X/100 = (400000 - 10X)/100
15X = 400000 - 10X
15X + 10X = 400000
25X = 400000
X = Rs. 16,000

Amount invested in scheme B = 40000 - X
= 40000 - 16000
= Rs. 24,000
Therefore, Rs. 24,000 invested in scheme B.
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51. Rs. 2500 was borrowed for 3 years. What will be the compound interest if the rate of interest for first year is 3% per annum, second year is 4% per annum and for third year is 5% per annum respectively?




SHOW ANSWER
Correct Ans:311.9
Explanation:
Given: Pricipal = Rs. 2500
r₁ = 3%; r₂ = 4%; r₃ = 5%
WKT, Amount = P[1 + (R/100)]n
A = P{(1 + (r₁/100)) * (1 + (r₂/100)) * (1 + (r₃/100))}
= 2500{(1 + (3/100)) * (1 + (4/100)) * (1 + (5/100))}
= 2500(103/100) * (104/100) * (105/100)
A = Rs. 2811.90
CI = Amount - Principal
CI = 2811.90 - 2500
CI = Rs. 311.90
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52. Calculate the amount for Rs. 37,500 at the of 8% per annum compound interest compounded half yearly for 1(1/2) years.




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Correct Ans:Rs. 42,812.4
Explanation:
Rate = r = 8% p.a = 4% per half-year
Time = n = 3/2 years = 3 half years
Formula for amount, A = P(1+(r/100))ⁿ
= 37500 (1+(4/100))³
= 37500 (1+(1/25))³
= 37500 (26/25)³
= Rs. 42812.4
Therefore, amount A = Rs. 42812.4
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53. Manju saves Rs. 200 at the end of each year and lends the money at 5% compound interest. How much it will become at the end of 3 years? 




SHOW ANSWER
Correct Ans:Rs. 662.02
Explanation:
Given: P = 220, R = 5%
WKT, Amount = P[1 + (R/100)]n
Amount = [200(1 + (5/100))3] + [200(1 + (5/100))2] + [200(1 + (5/100)]
= [200(1 + (1/20))3] + [200(1 + (1/20))2] + [200(1 + (1/20)]
= [200(21/20)3] + [200(21/20)2] + [200(21/20)]
= [(200*9261)/8000] + [(200* 441)/400] + [210]
= 231.525 + 220.5 + 210
= Rs. 662.025
Therefore amount at the end of 3 years be Rs. 662.025.
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54. A sum of money amounts to Rs. 4840 in 2 yr and to Rs. 5324 in 3 yr at compound interest compounded annually. The rate of interest per annum is 




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Correct Ans:10%
Explanation:
Let the rate of interest be r% per annum.
WKT, Amount = P[1 + (R/100)]n
Sum of money amounts to Rs. 4840 in 2 yr,
4840 = P[1 + (r/100)]2 ....(i)
Sum of money amounts to Rs. 5324 in 3 yr,
5324 = P[1 + (r/100)]3 .....(ii)
Dividing equation (ii) by (i), we get
5324/4840 = 1 + (r/100)
(5324/4840) - 1 = (r/100)
(5324 - 4840)/4840 = (r/100)
484/4840 = r/100
r = (484/4840)*100
r = 10%
Therefore, rate of interest per annum is 10%.
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Study the following information carefully and answer the given questions:
A man invested Rs. 30000 in a scheme at 20% compound interest for 2 years. After 2 years he withdraws all his money. From that money, he purchased a Bike worth Rs. 32000. And with remaining amount, 10% in mutual funds and with the remaining money, he purchased 2 watches W1 and W2 for an equal amount. He sells watch W1 at 10% profit and watches W2 at 20% profit.



Refer the above for the Questions 55 to 54
55. Find the Selling price of watch 2?




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Correct Ans:Rs. 6048
Explanation:
The principle amount = Rs.30000
Compound interest:
30000 * (20/100)= 6000
36000 * (20/100)= 72000
Compound Interest = 6000 + 7200
C.I = Rs.13200
The amount received after 2 years of his investment = 30000 + 13200 = Rs. 43200
It is given that, he purchased a Bike worth Rs.32000
Remaining amount = 43200 – 32000 = Rs.11200
Total amount invested in Mutual funds = 11200*(10/100) = Rs. 1120
Remaining amount = 11200 – 1120 = Rs. 10080
With this remaining amount, he purchased 2 watches W1 and W2 for an equal amount.
Cost price of W1 = Cost price of W2 = 10080/2 = Rs.5040
Selling price of W1 = 5040*(110/100) = Rs.5544
Selling price of W2 = 5040*(120/100) = Rs. 6048
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Study the following information carefully and answer the given questions:
A man invested Rs. 30000 in a scheme at 20% compound interest for 2 years. After 2 years he withdraws all his money. From that money, he purchased a Bike worth Rs. 32000. And with remaining amount, 10% in mutual funds and with the remaining money, he purchased 2 watches W1 and W2 for an equal amount. He sells watch W1 at 10% profit and watches W2 at 20% profit.



Refer the above for the Questions 56 to 55
56. Find the Selling price of watch 1?




SHOW ANSWER
Correct Ans:Rs. 5544
Explanation:
The principle amount = Rs.30000
Compound interest:
30000 * (20/100)= 6000
36000 * (20/100)= 72000
Compound Interest = 6000 + 7200
C.I = Rs.13200
The amount received after 2 years of his investment = 30000 + 13200 = Rs. 43200
It is given that, he purchased a Bike worth Rs.32000
Remaining amount = 43200 – 32000 = Rs.11200
Total amount invested in Mutual funds = 11200*(10/100) = Rs. 1120
Remaining amount = 11200 – 1120 = Rs. 10080
With this remaining amount, he purchased 2 watches W1 and W2 for an equal amount.
Cost price of W1 = Cost price of W2 = 10080/2 = Rs.5040
Selling price of W1 = 5040*(110/100) = Rs.5544
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Study the following information carefully and answer the given questions:
A man invested Rs. 30000 in a scheme at 20% compound interest for 2 years. After 2 years he withdraws all his money. From that money, he purchased a Bike worth Rs. 32000. And with remaining amount, 10% in mutual funds and with the remaining money, he purchased 2 watches W1 and W2 for an equal amount. He sells watch W1 at 10% profit and watches W2 at 20% profit.



Refer the above for the Questions 57 to 56
57. Find the amount he invested in mutual funds?




SHOW ANSWER
Correct Ans:Rs. 1120
Explanation:
The principle amount = Rs.30000
Compound interest:
30000 * (20/100)= 6000
36000 * (20/100)= 72000
Compound Interest = 6000 + 7200
C.I = Rs.13200
The amount received after 2 years of his investment = 30000 + 13200 = Rs. 43200
It is given that, he purchased a Bike worth Rs.32000
Remaining amount = 43200 – 32000 = Rs.11200
Total amount invested in Mutual funds = 11200*(10/100) = Rs. 1120
Remaining amount = 11200 – 1120 = Rs. 10080
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Study the following information carefully and answer the given questions:
A man invested Rs. 30000 in a scheme at 20% compound interest for 2 years. After 2 years he withdraws all his money. From that money, he purchased a Bike worth Rs. 32000. And with remaining amount, 10% in mutual funds and with the remaining money, he purchased 2 watches W1 and W2 for an equal amount. He sells watch W1 at 10% profit and watches W2 at 20% profit.



Refer the above for the Questions 58 to 57
58. Find the amount left after buying a bike?




SHOW ANSWER
Correct Ans:Rs. 11200
Explanation:
The principle amount = Rs.30000
Compound interest:
30000 * (20/100)= 6000
36000 * (20/100)= 72000
Compound Interest = 6000 + 7200
C.I = Rs.13200
The amount received after 2 years of his investment = 30000 + 13200 = Rs. 43200
It is given that, he purchased a Bike worth Rs.32000
Remaining amount = 43200 – 32000 = Rs.11200
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Study the following information carefully and answer the given questions:
A man invested Rs. 30000 in a scheme at 20% compound interest for 2 years. After 2 years he withdraws all his money. From that money, he purchased a Bike worth Rs. 32000. And with remaining amount, 10% in mutual funds and with the remaining money, he purchased 2 watches W1 and W2 for an equal amount. He sells watch W1 at 10% profit and watches W2 at 20% profit.



Refer the above for the Questions 59 to 58
59. Find the amount received after 2 years of his investment?




SHOW ANSWER
Correct Ans:Rs. 43200
Explanation:
The principle amount = Rs.30000
Compound interest:
30000 * (20/100)= 6000
36000 * (20/100)= 72000
Compound Interest = 6000 + 7200
C.I = Rs.13200
The amount received after 2 years of his investment = 30000 + 13200 = Rs. 43200
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60. Reet invested an amount of Rs A for 2 years at 12% compound interest and received some amount of interest. Sonali invested Rs (A + 1500) for 3 years at 8% simple interest and received same amount of interest as Reet received. Find the amount that is invested by Reet. 




SHOW ANSWER
Correct Ans:Rs. 25,000
Explanation:

Reet invested an amount = Rs.A
Sonali invested an amount = Rs. (A + 1500)
According to the question, same amount of interest is received by both.
Therefore, CI = SI
P[1 + (R/100)]ⁿ - P = PNR/100
A(1 + (12/100))² - A = [(A + 1500)*3*8%]
A*(112/100)*(112/100) - A = (A + 1500)*(24/100)
A*(12544/10000) - A = A*(24/100) + (1500*(24/100))
A*(12544/10000) - A - A*(24/100) = 360
(12544A - 10000A - 2400A)/10000 = 360
144A = 3600000
A = Rs. 25,000
Amount invested by Reet = Rs. 25,000.

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