A certain sum of money amounts to ₹815 in 3 years and to ₹854 in 4 years at simple interest. What is the principal amount?
Explanation: SI for 1 year = ₹854 − ₹815 = ₹39. For 3 years, SI = ₹117. Principal = ₹815 − ₹117 = ₹698.
What is the compound interest on ₹25,000 for 2 years at 12% per annum compounded annually?
Explanation: Amount = ₹25,000 × (1.12)² = ₹31360. CI = ₹6360. SI would be ₹6000.
What is the compound interest on ₹15,000 for 1 year at 10% per annum compounded half-yearly?
- ₹1,575.00
- ₹1,500.00
- ₹1,650.00
- ₹1,537.50
Explanation: Rate per half-year = 5%, periods = 2. Amount = ₹15,000 × (1.05)² = ₹16537.50. CI = ₹1537.50.
What is the difference between compound interest and simple interest on ₹5,000 for 2 years at 8% per annum?
Explanation: SI = ₹800, CI = ₹832. Difference = ₹32. Shortcut: P×(R/100)² = ₹5,000×0.0064 = ₹32.
The difference between compound interest and simple interest on a certain sum for 3 years at 10% per annum is ₹31. What is the sum?
Explanation: CI = ₹331, SI = ₹300, Difference = ₹31. With P = ₹1000, r = 10%: ₹331 − ₹300 = ₹31.
At what rate percent per annum simple interest will a sum of money double itself in 5 years?
Explanation: If sum doubles, Interest = Principal. Using SI = P×r×t/100: P = P×r×5/100, so r = 20%.
In how much time will a sum of ₹800 amount to ₹960 at 8% per annum simple interest?
- 2 years
- 3.5 years
- 3 years
- 2.5 years
Explanation: SI = ₹960 − ₹800 = ₹160. t = (SI×100)/(P×R) = (160×100)/(800×8) = 2.5 years.
What is the compound interest on ₹10,000 for 6 months at 20% per annum compounded quarterly?
- ₹1,000
- ₹1,050
- ₹2,000
- ₹1,025
Explanation: Quarterly: rate per quarter = 5%, periods = 2. Amount = ₹10,000 × (1.05)² = ₹11025. CI = ₹1025.
What is the effective annual rate corresponding to a nominal rate of 20% per annum compounded half-yearly?
Explanation: Effective rate = (1 + r/n)ⁿ − 1 = (1.10)² − 1 = 1.21 − 1 = 21%.
The population of a town is 50,000. It increases at the rate of 4% per annum. What will be the population after 2 years?
- 51,000
- 54,080
- 54,000
- 52,080
Explanation: Population = 50,000 × (1.04)² = 50,000 × 1.0816 = 54080.
A machine worth ₹80,000 depreciates at the rate of 10% per annum. What will be its value after 2 years?
- ₹64,800
- ₹69,600
- ₹72,000
- ₹68,000
Explanation: Value = ₹80,000 × (0.90)² = ₹80,000 × 0.81 = ₹64800.
The simple interest on a sum of ₹10,000 for 2 years at 12% per annum is equal to the compound interest on the same sum for 1 year at a certain rate compounded annually. What is that rate?
Explanation: SI = ₹10,000 × 12% × 2 = ₹2,400. For CI in 1 year: ₹10,000 × r/100 = ₹2,400, so r = 24%.
Two equal sums of ₹5,000 each are lent out at simple interest, one at 8% and the other at 12% per annum, both for 4 years. What is the total interest earned?
- ₹4,800
- ₹3,200
- ₹4,000
- ₹2,000
Explanation: Interest from first = ₹5,000 × 8% × 4 = ₹1600. From second = ₹5,000 × 12% × 4 = ₹2400. Total = ₹4000.
The simple interest on a sum of ₹10,000 at 10% per annum amounts to the same as the compound interest on the same sum for 1 year at 20% per annum compounded annually. What is the time period for the simple interest?
- 3 years
- 1 year
- 2.5 years
- 2 years
Explanation: CI for 1 year at 20% = ₹2,000. For SI: ₹2,000 = ₹10,000 × 10% × t, so t = 2 years.
A loan of ₹21,000 at 10% compound interest is to be repaid in two equal annual installments. What is the amount of each installment?
- ₹10,500
- ₹12,500
- ₹12,100
- ₹11,500
Explanation: Let installment = x. ₹21,000 × (1.10)² = x(1.10) + x. ₹25410 = 2.1x, so x = ₹12100.
At what rate of compound interest per annum will a sum of money double in approximately 3 years?
Explanation: (1+r)³ = 2, so 1+r = 2^(1/3) ≈ 1.2599, giving r ≈ 26.0%.
A sum invested at compound interest amounts to ₹8,820 in 2 years and to ₹9,261 in 3 years. What is the principal?
- ₹8,000
- ₹8,500
- ₹8,640
- ₹7,500
Explanation: Ratio = ₹9,261/₹8,820 = 1.05, so rate = 5.000000000000004%. Principal = ₹8,820/(1.05)² = ₹8000.
The compound interest on a certain sum for 2 years is ₹210 and for 3 years is ₹331. What is the rate of interest?
Explanation: CI for 3rd year = ₹331 − ₹210 = ₹121. This is interest on amount after 2 years: ₹1210 × r/100 = ₹121, so r = 10%. Verification: ₹1,000 × (1.10)² − ₹1,000 = ₹210. ✓
A sum of ₹6,000 yields a simple interest of ₹1,800 in 3 years. What is the rate of interest per annum?
Explanation: Rate = (SI × 100)/(P × t) = (1,800 × 100)/(6,000 × 3) = 180,000/18,000 = 10%.
What is the amount on ₹4,500 at 8% per annum simple interest for 2.5 years?
- ₹5,400
- ₹5,500
- ₹5,200
- ₹5,800
Explanation: SI = ₹4,500 × 8% × 2.5 = ₹900. Amount = ₹4,500 + ₹900 = ₹5400.
A sum amounts to ₹13,310 in 3 years at 10% per annum compound interest compounded annually. What is the principal?
- ₹12,000
- ₹9,999
- ₹10,500
- ₹11,000
Explanation: P = ₹13,310/(1.10)³ = ₹13,310/1.331 = ₹9999.
₹5,000 is lent at 6% per annum for the first 2 years and at 8% per annum for the next 3 years at simple interest. What is the total interest?
- ₹1,800
- ₹2,000
- ₹1,500
- ₹1,900
Explanation: Interest for first 2 years = ₹5,000 × 6% × 2 = ₹600. For next 3 years = ₹5,000 × 8% × 3 = ₹1,200. Total = ₹1800.
What is the compound interest on ₹8,000 for 1 year at 20% per annum compounded half-yearly?
- ₹1,690
- ₹1,860
- ₹2,000
- ₹1,680
Explanation: Rate per half-year = 10%, periods = 2. Amount = ₹8,000 × (1.10)² = ₹9680. CI = ₹1680.
In how much time will ₹2,400 amount to ₹3,000 at 10% per annum simple interest?
- 3.5 years
- 2.5 years
- 3 years
- 2 years
Explanation: SI = ₹3,000 − ₹2,400 = ₹600. t = (600 × 100)/(2,400 × 10) = 2.5 years.
A sum of ₹10,000 invested at compound interest compounded quarterly amounts to ₹10,824.32 in 1 year. What is the rate of interest?
Explanation: (1 + r/400)⁴ = ₹10,824.32/₹10,000 = 1.082432. Since (1.02)⁴ = 1.082432, r/400 = 0.02, so r = 8%.
A sum of money doubles itself in 8 years at simple interest. In how many years will it triple itself?
- 20 years
- 16 years
- 24 years
- 12 years
Explanation: If the sum doubles in 8 years, the interest earned in 8 years equals the principal. To triple, we need interest equal to 2×principal, which takes 2 × 8 = 16 years.
What is the difference in compound interest on ₹10,000 for 2 years at 20% per annum when compounded half-yearly versus compounded annually?
Explanation: Annual CI = ₹4400. Half-yearly: Amount = ₹10,000 × (1.10)⁴ = ₹14641, CI = ₹4641. Difference = ₹241.
The simple interest on a sum for 3 years at 12% per annum is ₹720. What is the sum?
- ₹2,500
- ₹1,800
- ₹2,000
- ₹2,200
Explanation: P = (SI × 100)/(R × T) = (720 × 100)/(12 × 3) = ₹2000.
A sum amounts to ₹10,648 in 3 years at 10% per annum compound interest. What is the compound interest for 2 years on the same sum at the same rate?
- ₹1,800
- ₹1,680
- ₹1,500
- ₹2,080
Explanation: P = ₹10,648/(1.10)³ = ₹7999. CI for 2 years = ₹7999 × [(1.10)² − 1] = ₹1680.
The simple interest on ₹4,000 for 3 years is equal to the simple interest on ₹5,000 for a certain period at the same rate. What is that period?
- 2 years
- 3.6 years
- 4 years
- 2.4 years
Explanation: Since SI is equal: ₹4,000 × 3 = ₹5,000 × t₂. So t₂ = 12,000/5,000 = 2.4 years.
The compound interest on a certain sum for 3 years at 5% per annum is ₹1,261. What is the sum?
- ₹9,000
- ₹7,999
- ₹8,500
- ₹7,699
Explanation: P = CI/[(1+r)³ − 1] = ₹1,261/[(1.05)³ − 1] = ₹1,261/0.157625 = ₹7999.
A sum of ₹4,000 amounts to ₹5,600 in 5 years at simple interest. What is the rate of interest?
Explanation: SI = ₹5,600 − ₹4,000 = ₹1600. Rate = (1,600 × 100)/(4,000 × 5) = 8.0%.
In how many years will ₹8,000 amount to ₹15,625 at 25% per annum compound interest compounded annually?
- 4 years
- 3.5 years
- 3 years
- 2 years
Explanation: ₹8,000 × (1.25)³ = ₹8,000 × 1.953125 = ₹15,625. So t = 3 years.
What is the simple interest per month on ₹12,000 at 12% per annum?
Explanation: Monthly interest = ₹12,000 × 12% / 12 = ₹120. Common error: ₹144 is the yearly interest divided by 12 months but using wrong principal, or confusing with annual amount.
What is the compound interest on ₹15,000 for 3 years at 12% per annum compounded annually?
Explanation: Amount = ₹15,000 × (1.12)³ = ₹15,000 × 1.404928 = ₹21073. CI = ₹6073.
The simple interest on a sum for 3 years at 10% per annum is equal to the simple interest on the same sum for 2 years at a certain rate. What is that rate?
Explanation: Since SI is equal: P × 10% × 3 = P × r × 2. So 30 = 2r, giving r = 15%.
What is the compound interest on ₹20,000 for 1.5 years at 10% per annum compounded half-yearly?
- ₹3,200
- ₹3,000
- ₹3,152
- ₹3,562
Explanation: Rate per half-year = 5%, periods = 3. Amount = ₹20,000 × (1.05)³ = ₹23152. CI = ₹3152.
₹10,000 is invested at 8% and ₹15,000 at 12% per annum simple interest, both for 2 years. What is the average rate of interest on the total investment?
Explanation: Total interest = ₹5200. Average rate = (5200 × 100)/(₹25,000 × 2) = 10.4%.
A sum invested at 20% per annum compounded half-yearly amounts to ₹12,100 in 1 year. What is the principal?
- ₹11,000
- ₹10,500
- ₹9,999
- ₹9,500
Explanation: P = ₹12,100/(1.10)² = ₹12,100/1.21 = ₹9999.
What is the simple interest earned in the 3rd year on a sum of ₹5,000 at 10% per annum simple interest?
Explanation: In simple interest, interest is the same every year: ₹5,000 × 10% = ₹500. Distractor ₹550 = adding 10% to ₹500 incorrectly.
What is the compound interest earned in the 2nd year on a sum of ₹10,000 at 10% per annum compound interest?
- ₹1,200
- ₹2,000
- ₹1,000
- ₹1,100
Explanation: Amount after 1 year = ₹11000. Interest in 2nd year = ₹11000 × 10% = ₹1100.
₹6,000 is lent at simple interest at 5% for the first year, 8% for the second year, and 10% for the third year. What is the total amount after 3 years?
- ₹7,500
- ₹7,980
- ₹7,200
- ₹7,380
Explanation: Interest = ₹6,000 × (5% + 8% + 10%) = ₹6,000 × 23% = ₹1380. Amount = ₹6,000 + ₹1380 = ₹7380.
What is the difference between compound interest and simple interest on ₹12,000 for 2 years at 10% per annum?
Explanation: SI = ₹2400, CI = ₹2520. Difference = ₹120. Shortcut: ₹12,000 × (0.10)² = ₹120.
A sum of ₹4,000 amounts to ₹5,000 in 2.5 years at simple interest. What is the rate of interest?
Explanation: SI = ₹1,000. Rate = (1,000 × 100)/(4,000 × 2.5) = 10%.
A sum of ₹25,000 amounts to ₹28,090 in 2 years at compound interest compounded annually. What is the rate of interest?
Explanation: (1+r)² = ₹28,090/₹25,000 = 1.1236. Since 1.06² = 1.1236, r = 6%.
In how many years will a sum of money become 5/4 of itself at 5% per annum simple interest?
- 3 years
- 4 years
- 5 years
- 6 years
Explanation: SI = (5/4)P − P = P/4. Using SI = P×r×t/100: P/4 = P×5×t/100, so t = 100/20 = 5 years.
The compound interest on a certain sum for 2 years at 15% per annum is ₹3,225. What is the sum?
- ₹10,000
- ₹15,000
- ₹12,000
- ₹8,000
Explanation: P = CI/[(1+r)² − 1] = ₹3,225/[(1.15)² − 1] = ₹3,225/0.3225 = ₹10000.
A invests ₹8,000 at 10% per annum simple interest for 3 years. B invests ₹10,000 at 8% per annum simple interest for 2 years. What is the difference in interest earned?
Explanation: A's interest = ₹8,000 × 10% × 3 = ₹2400. B's interest = ₹10,000 × 8% × 2 = ₹1600. Difference = ₹800.
₹10,000 is invested at compound interest at 10% for the first year and 12% for the second year. What is the compound interest after 2 years?
- ₹2,820
- ₹2,200
- ₹2,000
- ₹2,320
Explanation: Amount = ₹10,000 × 1.10 × 1.12 = ₹12320. CI = ₹2320.
A sum amounts to ₹7,500 in 2.5 years at 10% per annum simple interest. What is the principal?
- ₹7,000
- ₹6,500
- ₹6,000
- ₹5,500
Explanation: P + P×10%×2.5 = ₹7,500. P×1.25 = ₹7,500. P = ₹6000.
In how many years will ₹10,000 amount to ₹14,641 at 10% per annum compound interest compounded annually?
- 4 years
- 3 years
- 5 years
- 3.5 years
Explanation: ₹10,000 × (1.10)⁴ = ₹10,000 × 1.4641 = ₹14,641. So t = 4 years.
A sum of money amounts to 7/4 of itself in 5 years at simple interest. What is the rate of interest?
Explanation: SI = (7/4)P − P = 3P/4. Rate = [(3P/4) × 100]/(P × 5) = 75/5 = 15%.
A sum of ₹8,000 amounts to ₹10,648 in 3 years at compound interest compounded annually. What is the rate of interest?
Explanation: (1+r)³ = ₹10,648/₹8,000 = 1.331. Since 1.1³ = 1.331, r = 10%.
₹3,000 and ₹5,000 are invested at 8% and 12% per annum simple interest respectively for 3 years. What is the total interest earned?
- ₹2,520
- ₹2,000
- ₹3,000
- ₹2,500
Explanation: Interest from first = ₹3,000 × 8% × 3 = ₹720. From second = ₹5,000 × 12% × 3 = ₹1,800. Total = ₹2520.
A sum invested at 8% for the first year and 10% for the second year at compound interest amounts to ₹11,880. What is the principal?
- ₹12,099
- ₹9,999
- ₹9,000
- ₹11,000
Explanation: P × 1.08 × 1.10 = ₹11,880. P = ₹11,880/1.188 = ₹9999.
In how much time will ₹3,600 amount to ₹4,680 at 10% per annum simple interest?
- 3.5 years
- 3 years
- 2 years
- 4 years
Explanation: SI = ₹1,080. t = (1,080 × 100)/(3,600 × 10) = 3 years.
What is the compound interest on ₹4,000 for 3 years at 20% per annum compounded half-yearly?
- ₹3,290
- ₹2,800
- ₹2,400
- ₹3,086
Explanation: Rate per half-year = 10%, periods = 6. Amount = ₹4,000 × (1.10)⁶ = ₹7086. CI = ₹3086.
A sum of money amounts to 9/5 of itself in 4 years at simple interest. What is the rate of interest?
Explanation: SI = (9/5)P − P = 4P/5. Rate = [(4P/5) × 100]/(P × 4) = 80/4 = 20%.
The compound interest on a certain sum for 3 years at 10% per annum is ₹3,310. What is the sum?
- ₹9,999
- ₹8,000
- ₹15,000
- ₹12,000
Explanation: P = CI/[(1+r)³ − 1] = ₹3,310/[(1.10)³ − 1] = ₹3,310/0.331 = ₹9999.
The simple interest on ₹7,500 for 3 years is ₹2,250. What is the rate of interest per annum?
Explanation: Rate = (2,250 × 100)/(7,500 × 3) = 10%.