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[Concept: Effective CI Rate for 2 Years] If the rate of interest is 10% per annum, what is the effective compound interest rate for 2 years?
- 21%
- 20%
- 22%
- 21.5%
Explanation: Book Formula for same rate over 2 years: CI_2 = (2r + r²/100)%. Here r = 10. CI_2 = (2*10 + 100/100)% = (20 + 1)% = 21%.
[Concept: Effective CI Rate for 2 Years] What is the compound interest on Rs 8000 for 2 years if the rate of interest is 5% in the first year and 8% in the second year?
- Rs 1072
- Rs 1040
- Rs 1100
- Rs 1080
Explanation: Book Formula for different rates: CI_2 = (x + y + xy/100)%. Here x = 5, y = 8. Effective rate = 5 + 8 + (40/100) = 13.4%. CI = 13.4% of 8000 = (13.4/100) * 8000 = 13.4 * 80 = Rs 1072.
[Concept: Effective CI Rate for 2 Years] A man invests Rs 5000 at 15% per annum compound interest. What will be the total interest earned at the end of 2 years?
- Rs 1612.5
- Rs 1500
- Rs 1600
- Rs 1550.5
Explanation: Formula: CI_2 = (2r + r²/100)%. Here r = 15. Effective rate = (30 + 225/100) = 32.25%. CI = 32.25% of 5000 = 32.25 * 50 = Rs 1612.5.
[Concept: Difference between CI & SI – 2 Years] The difference between Compound Interest and Simple Interest on a sum of Rs 7500 for 2 years is Rs 42. If the rate of interest is the same for both years, find the rate of interest per annum.
- 7.48% (Approx) / Using Formula
- 8%
- 7%
- 6%
Explanation: Book Formula: CI – SI for 2 years = P * (r/100)². We are given Diff = 42, P = 7500. So, 42 = 7500 * (r²/10000). 42 = 0.75 * r². r² = 42 / 0.75 = 56. r = √56 ≈ 7.48%. (Note: If rates were 7% and 8% as per book example, Diff = 7500 * (7*8/100)% = 7500 * 0.56% = 42).
[Concept: Difference between CI & SI – 2 Years] What is the difference between CI and SI on Rs 10000 for 2 years at the rate of 12% per annum?
- Rs 144
- Rs 120
- Rs 100
- Rs 150
Explanation: Book Formula: Difference for 2 years = P * (R/100)². Diff = 10000 * (12/100)² = 10000 * (144 / 10000) = Rs 144.
[Concept: Difference between CI & SI – 2 Years] If the difference between the CI and SI on a certain sum of money for 2 years at 5% per annum is Rs 25, find the principal sum.
- Rs 10000
- Rs 12500
- Rs 8000
- Rs 5000
Explanation: Formula: Diff = P * (R/100)². Here Diff = 25, R = 5. So, 25 = P * (25 / 10000). P = (25 * 10000) / 25 = Rs 10000.
[Concept: Difference between CI & SI – 3 Years] What is the difference between the Compound Interest and Simple Interest on Rs 5000 for 3 years at the rate of 10% per annum?
- Rs 155
- Rs 150
- Rs 165
- Rs 100
Explanation: Book Formula: For 3 years, CI – SI = P * (R/100)² * (3 + R/100). Diff = 5000 * (10/100)² * (3 + 10/100) = 5000 * (1/100) * (3.1) = 50 * 3.1 = Rs 155. (Alternatively from table: Diff % = 3.1%. 3.1% of 5000 = 155).
[Concept: Difference between CI & SI – 3 Years] The difference between CI and SI on a sum of money for 3 years at 20% per annum is Rs 640. What is the principal sum?
- Rs 5000
- Rs 4000
- Rs 6000
- Rs 8000
Explanation: From the book’s table, the difference % between CI and SI for 3 years at 20% is 12.8%. Therefore, 12.8% of P = 640. P = (640 / 12.8) * 100 = 50 * 100 = Rs 5000.
[Concept: Difference between CI & SI – 3 Years] If the difference between CI and SI on Rs 8000 for 3 years is Rs 61, what is the rate of interest per annum?
- 5%
- 10%
- 4%
- 8%
Explanation: Diff% = (61 / 8000) * 100 = 610/800 = 0.7625%. Looking at the book’s table, a difference of 0.7625% for 3 years exactly corresponds to a 5% rate of interest.
[Concept: Half-yearly/Quarterly CI] Find the amount on Rs 10000 for 1 year at 20% per annum, compounded half-yearly.
- Rs 12100
- Rs 12000
- Rs 12200
- Rs 11000
Explanation: Book Rule: If compounded half-yearly, Rate becomes R/2 = 20/2 = 10%. Time becomes T*2 = 1*2 = 2 cycles. Effective rate for 2 cycles at 10% is 21%. Amount = 10000 + 21% of 10000 = 10000 + 2100 = Rs 12100.
[Concept: Half-yearly/Quarterly CI] What will be the compound interest on Rs 16000 for 9 months at 20% per annum, if interest is compounded quarterly?
- Rs 2522
- Rs 2400
- Rs 2500
- Rs 2600
Explanation: Book Rule: If compounded quarterly, Rate = R/4 = 20/4 = 5% per quarter. Time = 9 months = 3 quarters. The effective CI rate for 3 cycles at 5% (from the table) is 15.7625%. CI = 15.7625% of 16000 = 15.7625 * 160 = Rs 2522.
[Concept: Half-yearly/Quarterly CI] A man invested Rs 20000 at 12% p.a. compounded monthly for 2 months. What is the compound interest earned?
- Rs 402
- Rs 400
- Rs 420
- Rs 404
Explanation: Book Rule: Compounded monthly, Rate = R/12 = 12/12 = 1% per month. Time = 2 months = 2 cycles. Effective rate for 2 cycles at 1% = (1+1+(1*1)/100) = 2.01%. CI = 2.01% of 20000 = 2.01 * 200 = Rs 402.
[Concept: Sum becomes ‘m’ times] A certain sum becomes 3 times of itself in 4 years on compound interest. In how many years will it become 27 times of itself?
- 12 years
- 16 years
- 8 years
- 20 years
Explanation: Book Concept: If a sum becomes ‘m’ times in ‘t’ years, it will become m^n times in (t*n) years. Here, it becomes 3 times in 4 years. We want 27 times, which is 3^3. Therefore, time = 4 * 3 = 12 years.
[Concept: Sum becomes ‘m’ times] A sum of money placed at compound interest doubles itself in 5 years. In how many years will it amount to 8 times itself?
- 15 years
- 20 years
- 10 years
- 12 years
Explanation: It becomes 2 times in 5 years. We want 8 times, which is 2^3. So, time required = 5 * 3 = 15 years.
[Concept: Sum becomes ‘m’ times] At compound interest, a sum becomes 4 times of itself in 6 years. How many times of itself will it become in 18 years?
- 64 times
- 32 times
- 16 times
- 12 times
Explanation: Time given is 18 years, which is 6 * 3 (t * n, so n=3). Therefore, the sum will become m^n times. m = 4. Amount = 4^3 = 64 times.
[Concept: Finding Rate R%] If a certain sum of money becomes 1.44 times of itself in 2 years on compound interest, what is the rate of interest?
- 20%
- 12%
- 44%
- 22%
Explanation: Book Formula: R% = [(B/A)^(1/n) – 1] * 100%. Here, B/A = 1.44, n = 2. R% = [√(1.44) – 1] * 100% = [1.2 – 1] * 100% = 0.2 * 100% = 20%.
[Concept: Finding Rate R%] A sum of money becomes 8 times of itself in 3 years at compound interest. Find the rate of interest per annum.
- 100%
- 50%
- 200%
- 80%
Explanation: Book Formula: R% = [(n)^(1/t) – 1] * 100%. Here n = 8, t = 3. R% = [(8)^(1/3) – 1] * 100% = [2 – 1] * 100% = 1 * 100% = 100%.
[Concept: Finding Rate R%] If a sum of Rs 8000 amounts to Rs 9261 in 3 years at compound interest, what is the rate percent per annum?
- 5%
- 10%
- 8%
- 4%
Explanation: Formula: R% = [(B/A)^(1/n) – 1] * 100%. Here B = 9261, A = 8000, n = 3. B/A = 9261/8000. Cube root of (9261/8000) = 21/20. R% = [21/20 – 1] * 100% = (1/20) * 100% = 5%.
[Concept: CI with Fractional Years] What will be the amount on Rs 10000 for 2.5 years (2 and 1/2 years) at 10% per annum compound interest?
- Rs 12705
- Rs 12500
- Rs 12605
- Rs 12100
Explanation: Book Formula: A = P * (1 + r/100)^n * (1 + rF/100). Here n = 2 full years, F = 1/2 year. A = 10000 * (1 + 10/100)² * (1 + (10*0.5)/100) = 10000 * (11/10)² * (1 + 5/100) = 10000 * (121/100) * (105/100) = 121 * 105 = Rs 12705.
[Concept: CI with Fractional Years] Find the amount on Rs 5000 at 20% per annum compound interest for 1 year and 3 months (1.25 years).
- Rs 6300
- Rs 6200
- Rs 6500
- Rs 6000
Explanation: Here n = 1 full year, F = 3/12 = 1/4 year. Formula: A = P * (1 + r/100)^1 * (1 + r*F/100). A = 5000 * (120/100) * (1 + (20*0.25)/100) = 5000 * (6/5) * (1 + 5/100) = 6000 * (105/100) = 60 * 105 = Rs 6300.
[Concept: CI with Fractional Years] Calculate the compound interest on Rs 8000 for 1.5 years at 10% per annum, compounded annually.
- Rs 1240
- Rs 1200
- Rs 1210
- Rs 1250
Explanation: n = 1, F = 1/2. Amount = 8000 * (110/100) * (1 + (10*0.5)/100) = 8000 * (11/10) * (105/100) = 80 * 11 * 1.05 = 880 * 1.05 = Rs 9240. CI = Amount – Principal = 9240 – 8000 = Rs 1240.
[Concept: CI Installments] A sum of Rs 2100 is borrowed at 10% compound interest. It is to be paid back in 2 equal annual installments. What is the value of each installment?
- Rs 1210
- Rs 1100
- Rs 1050
- Rs 1200
Explanation: Book Formula for n=2 installments: P = Installment * [ (100/(100+r)) + (100/(100+r))² ]. Here P = 2100, r = 10. Let installment be x. 2100 = x * [ (10/11) + (100/121) ]. 2100 = x * [ (110+100)/121 ]. 2100 = x * (210/121). x = (2100 * 121) / 210 = 10 * 121 = Rs 1210.
[Concept: CI Installments] A loan of Rs 6800 is to be discharged in two equal annual installments. If the rate of interest is 12.5% compounded annually, find the value of each installment.
- Rs 4050
- Rs 3400
- Rs 4200
- Rs 3600
Explanation: r = 12.5% = 1/8. So, 100/(100+r) is the multiplier, which is 8/9. P = Installment(x) * [ (8/9) + (8/9)² ]. 6800 = x * [ 8/9 + 64/81 ]. 6800 = x * [ (72+64)/81 ]. 6800 = x * (136/81). x = (6800 * 81) / 136 = 50 * 81 = Rs 4050.
[Concept: CI Installments] A man borrows a sum of Rs 25220 and promises to pay it back in 3 equal annual installments at a 5% compound interest rate. Find the value of each installment.
- Rs 9261
- Rs 8000
- Rs 9000
- Rs 8500
Explanation: r = 5% = 1/20. Multiplier = 20/21. For n=3, P = x * [ (20/21) + (20/21)² + (20/21)³ ]. 25220 = x * [ 20/21 + 400/441 + 8000/9261 ]. 25220 = x * [ (8820 + 8400 + 8000) / 9261 ]. 25220 = x * (25220 / 9261). Therefore, x = Rs 9261.