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Aptitude β Compound Interest Question in Answer with Solution (English) COMPOUND INTEREST:Compound interest is calculated each period on the original principal and all Interest accumulated during post periods although the interest may be slated a yearly rate the compounding periods can be yearly, semiannually, quarterly or even continuously. Let Principal = P, Rate = R% per annum, Time = T Years, ο° When interest is compounded annually:π
Amount = P [1 + 100] T ο° When interest in compounded half-Yearly :π
/2
Amount = P [1 + 100] 2T ο° When interest in compounded quarterly :π
/4
Amount = P [1 + 100] 4T 1
ο° When interest in compounded annually but time is in fraction say 5 3 years. π
Amount = P [1 + 100]
5
1 π
3
Γ [1 + 100]
ο° When rates are different for different year say R, %, R2% & R3% for 1st, 2nd & 3rd year respectively. π
1
π
2
π
3
π
π
Amount = P [1 + 100] [1 + 100] [1 + 100] β¦β¦β¦β¦β¦β¦β¦β¦β¦..[1 + 100] ο° Present worth of Rs. A due T year, hence P=
π΄ [1+
π
]π 100
Important facts:π
ο Amount (A) = P+C.I. = P [1 + 100] T π
ο C.I. = P [(1 + 100) π β 1] ο If interest is payable for 1 year, then simple interest & compound interest will be equal. ο In interest is compounded half-yearly, then rate of interest will be half (R/2) & time will be 2 times (2T). ο In interest is compounded quarterly, then rate of interest will be half (R/4) & time will be 4 times (4T). ο The difference between compound interest & simple interest of a principle (P) in T year at R% per annual rate of interest is π
= P[(1 + 100) π β
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Γπ 100
β 1]
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Aptitude β Compound Interest Question in Answer with Solution (English) 1. Find compound interest on Rs. 8000 at 5 % per annum for 3 years, compounded annually. (A) Rs. 1250 (B) Rs. 1261 (C) Rs. 1200 (D) Rs. 1150 2. Find the compound interest on Rs. 15000 in 3 years at 5 % per annum, the interest being compounded half yearly? (A) Rs. 2300 (B) Rs. 2250 (C) Rs. 2395.40 (D) Rs. 2295.40 3. Find the compound interest on Rs. 20000 at 8 % per annum for 9 months compounded annually. (A) Rs. 1200 (B) Rs. 1224 (C) Rs. 1250 (D) Rs. 1150 4. If Rs. 500 amounts to Rs. 583.2 in 2 years compounded annually, find the rate of interest per annum? (A) 5 % (B) 8 % (C) 10 % (D) 4 % 5. If the simple interest on a sum of money at 4 % per annum for 2 years is Rs. 400, find the compound interest on the same sum for the same period at the same rate. (A) Rs. 400 (B) Rs. 408 (C) Rs. 450 (D) Rs. 500 6. In what time will Rs.7500 become Rs.8112 at rate of 4 % per annum compounded annually? (A) 2 Years (B) 3 Years (C) 2.5 Years (D) 3.5 Years 7. If Rs.10000 has been lent out at 10 % rate of interest for 3 years, the interest being compounded annually, what is the interest for the third year? (A) Rs. 1100 (B) Rs. 1150 (C) Rs. 1210 (D) Rs. 1250 8. The difference between simple interest and compound interest on Rs.1200 for one year at 10 % per annum reckoned half yearly is : (A) Rs. 2.5 (B) Rs. 3.75 (C) Rs. 3 (D) Rs. 4 9. The compound interest on Rs.30000 at 7 % per annum is Rs.4347. The period (in years) is : (A) 2 Years (B) 2.5 Years (C) 3 Years (D) 4 Years 10. A certain sum amounts to Rs.7350 in 2 years and Rs.8575 in 3 years. Find the sum. (A) Rs. 5500 (B) Rs. 5400 (C) Rs. 5300 (D) Rs. 5200 11. What is the principal amount which earns Rs.132 as compound interest for the second year at 10% per annum? (A) Rs.900 (B) Rs.1150 (C) Rs.1200 (D) Rs.1250
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Aptitude β Compound Interest Question in Answer with Solution (English) 12. Ram invested an amount of 15000 in amount of 15000 in a fixed deposit for 2 years at compound interest rate of 6% per annum. How much ram will get on the maturity of the fixed deposit? (A) Rs.16854 (B) Rs.16000 (C) Rs.17000 (D) Rs.17500 13. If Rs 15000 amounts to Rs 16224 in 2 years compounded annually, find the rate of interest per annum. (A) 3% (B) 4% (C) 5% (D) 6% 14. If Rs.1301 divide between A and B in such a way, 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. Then what will be the share of A. (A) Rs.500 (B) Rs.550 (C) Rs.676 (D) Rs.600 15. What will be the difference between simple and compound interest at 10% per annum on a sum of Rs.1000 after 4 years? (A) Rs.31 (B) Rs.32.10 (C) Rs.40.40 (D) Rs.64.10 16. In how many years will a sum of Rs 800 at 10% per annum compounded semi annually becomes Rs.926.10? (A) 1 year 6 month (B) 1 year 6 month (C) 2 years (D) 1 years 17. The compound interest on a certain sum for 2 years at 10% per annum is Rs.525. the simple interest on the same sum for double the time at half the rate percent per annum is: (A) Rs.400 (B) Rs.500 (C) Rs.600 (D) Rs.800 18. The difference between compound interest and simple interest on an amount of Rs 15000 for 2 years is Rs.96. what is the rate of interest per annum? (A) 8% (B) 6% (C) 5% (D) 4% 19. On a sum of money the simple interest for 2 years is Rs.660, while compound interest is Rs 696.30, the rate of interest being the same in both the cases. The rate of interest is: (A) 10% (B) 10.5% (C) 12% (D) 11% 20. A sum of money invested at compound interest amounts to Rs 800 in 3 years and to Rs 840 in 4 years. The rate of interest per annum is: (A) 25/4% (B) 10% (C) 25/2% (D) 8%
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Aptitude β Compound Interest Question in Answer with Solution (English) Answers 1. [B]
2. [C]
3. [B]
4. [B]
5. [B]
6. [A]
7. [C]
8. [C]
9. [A]
10. [B]
11. [C]
12. [A]
13. [B]
14. [C]
15. [D]
16. [A]
17. [B]
18. [A]
19. [D]
20. [A]
Solutions
1. C. I.
3
5
= 8000 [(1 + 100) β 1] 105 3
= 8000 [(100) β 1] = 1261 ο° In other way:A
5
= 8000 Γ (1 + 100)
3
105 3
= 8000 Γ (100) = 9261 C. I. 2. C. I.
= 9261 β 8000 = 1261 2.5 6
= 15000 [(1 + 100) β 1] 102.5 6
= 15000 [(
100
) β 1] = 2395.40
ο° In other way:A
2.5 6
= 15000 Γ (1 + 100) 102.5 6
= 15000 Γ ( 100 ) = 17395.40 β΄ C. I. = 17395.40 β 15000 = 2395.40 3. β΅ Principal = Rs. 20000, Time = 9 Months = 3 Quarters, Rate = 8 % per annum = 2 % per quarter C. I.
2
3
102 3
= 20000 [(1 + 100) β 1] = 20000 [(100) β 1] = Rs. 1224
4. Principal = Rs. 500, Amount = Rs. 583.2, Time = 2 Years, Let the rate be R % per annum. Then π
2
500 (1 + 100) = 583.2 βΉ βΉ βΉ βΉ βΉ βΉ
π
2
583.2
π
2
500 5832Γ2
2
500Γ2 108 2
(1 + 100) = (1 + 100) = π
=
11664 10000
(1 + 100) = (100) π
108 1+ = 100 100 100 + π
= 108 R = 108 β 100 = 8 %.
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Aptitude β Compound Interest Question in Answer with Solution (English) 5. Given, Rate = 4 % P.A., Time = 2 Years, S. I. = Rs. 400 100Γ400 So, P = 4Γ2 = 5000, 4
2
β΄ C. I. = 5000 [(1 + 100) β 1] 105 2
= 5000 [(100) β 1] = 408 π
4
6. 7500 (1 + 100) = 8112 104 π
8112
100 26 π
7500 676
26 π
625 26 2
βΉ
(
) =
βΉ
(25) =
βΉ
(25) = (25)
βΉ
T = 2 Year
676Γ12
{625Γ12}
7. Amount at the end of the second year will be the principal for the third year. β΄ Amount at the end of the second year π
2
10 2
110 2
= P (1 + 100) = 10000 (1 + 100) = 10000 (100)
= Rs. 12100 β΄ The interest on this sum for one year will be the interest for the third year. 10 1
β΄ Interest for the third year = 12100 [(1 + 100) β 1] = 12100 [0.1] = 1210 = Rs. 1210 8. S. I. = Rs. [
1200Γ10Γ1
] = π
π . 120
100
5
2
C. I. = Rs. [1200 (1 + 100) β 1200] = π
π . 123 Difference = Rs. (123 - 120) = Rs. 3 9. Amount = Rs. (30000 + 4347) = Rs. 34347 Let the Time be T Years. Then 7
π
30000 [1 + 100] = 34347 107 π
34347
11449
107 2
βΉ
[100] = 10030000 = 10000 = [100]
βΉ
T = 2 Years
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Aptitude β Compound Interest Question in Answer with Solution (English) 10. S. I. on Rs. 7350 for 1 Year = Rs. (8575 - 7350) = Rs. 1225 β΄ Rate = [
100Γ1225
2
] % = 16 3 %
7350Γ1
Let the sum be x then 2
50
π₯ [1 + 3Γ100] = 7350 7
67
π₯Γ6 Γ π₯=
6 7350Γ36 49
= 7350 = 5400
π₯ = π
π . 5400 11. Let the principal at the end of first year be π π Γ 10Γ 1 Then = = 132 βΉ π = 1320 100
Now let original principal P π Amount after 1 year = P + Hence
11π 10
= 1320
Γ 10Γ 1
=
100
11π 10
βΉ P = 1200 2
6
12. Amount = [15000 Γ (1 + 100) ] 53
53
= 15000 Γ 50 Γ 50 = 16854 13. Principal = Rs 15000, Amount = Rs 16224 , Time = 2 years Let the rate of interest per annum is R % 2
R
Than [15000 Γ (1 + 100) ] = 16224 R
2
16224
16224 Γ6
97344
312 2
βΉ (1 + 100) = 15000 = 15000 Γ6 = 90000 = [300] π
βΉ 1 + 100 = βΉR=
312
300 12 Γ100
π
312
12
βΉ 100 = 300 - = 300
4%
300
14. Let , the share of = π, Then the share of B = (1301 - π) 4
7
4
β΄ π [1 + 100] = (1301 β ) [1 + 100] βΉ
π³ (1301β π³)
4
2
26
= [1 + 100] = [25 Γ
9
26
]
25
βΉ 625 π = 676 Γ (1301 - π) βΉ 625 π = 676 Γ 1301 β 676 π βΉ 1301 π = 676 Γ 1301 π = 676 15. S.I. = Rs. [
1000 Γ10 Γ4 100
] = Rs.400 10 4
C.I. = Rs. [15000 Γ (1 + 100) β 1000] = Rs.464.10 β΄ Difference = Rs. (464.10 - 400) = 64.10
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Aptitude β Compound Interest Question in Answer with Solution (English) 16. Let the time be N years, then 5
800 Γ [1 + 100] 5
Or [1 + 100] 21 2n
Or [20]
2n
2n
=
= 926.10 926.10 800
21 3
9261
= 8000
= [20]
Or 2n = 3 3
1
Or n = 2 = 1 2 years 17. Let the sum be Rs. P, then, 10 2
[π Γ (1 + 100) β π] = 525 11 2
Or P [(10) β 1] = 525 121
Or P [100 β 1] = 525 121
Or p [100] = 525 Or P = β΄ S.I. =
525 Γ100
= 2500
21 2500 Γ5 Γ4
= 500
100
2
R
18. [15000 Γ (1 + 100) β 15000] - [ 2
R
15000 ΓR Γ2 100
] = 96
2π
Or 15000 [(1 + 100) β 1 β 100] = 96 Or 15000 [ Or R2 =
(100+π
)2 β10000β200R
96 Γ2 3
10000
] = 96
= 64 .......... On Solving
Or R = 8 β΄ Rate of interest is 8%. 19. Difference in C.I and S.I for 2 years = 696.30 β 660 = 36.30 S.I. for one year = = Rs.330 β΄ S.I. on Rs 330 for 1 year = 36.30 β΄ Rate = [
100 Γ36.30 330Γ1
]% = 11%
20. S.I. on Rs.800 for 1 year = Rs. (840 - 800) = Rs.40 100 Γ40
1
β΄ Rate = [ 800Γ1 ] % = 6 4%
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