Compound interest means interest on interest. It is a favourite in banking and aptitude exams.
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Q1. The difference between the compound interest and the simple interest on a certain sum for 3 years at 20% per annum is Rs 27648. Find the sum.
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Answer: C
Let the sum be P, Rate R = 20% per annum, Time = 3 years. For 3 years, the standard result is C.I. – S.I. = P x (R/100)^2 x (3 + R/100). Given C.I. – S.I. = Rs 27648, so 27648 = P x (20/100)^2 x (320/100). So P = (27648 x 1000000) / (400 x 320) = Rs 216000. Check: P x (R/100)^2 x (3+R/100) = 216000 x (20/100)^2 x (320/100) = Rs 27648, matching the given difference.
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Q2. The difference between the compound interest and the simple interest on a certain sum for 3 years at 15% per annum is Rs 1134. Find the sum.
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Answer: B
Let the sum be P, Rate R = 15% per annum, Time = 3 years. For 3 years, the standard result is C.I. – S.I. = P x (R/100)^2 x (3 + R/100). Given C.I. – S.I. = Rs 1134, so 1134 = P x (15/100)^2 x (315/100). So P = (1134 x 1000000) / (225 x 315) = Rs 16000. Check: P x (R/100)^2 x (3+R/100) = 16000 x (15/100)^2 x (315/100) = Rs 1134, matching the given difference.
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Q3. The difference between the compound interest and the simple interest on a certain sum for 3 years at 5% per annum is Rs 976. Find the sum.
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Answer: C
Let the sum be P, Rate R = 5% per annum, Time = 3 years. For 3 years, the standard result is C.I. – S.I. = P x (R/100)^2 x (3 + R/100). Given C.I. – S.I. = Rs 976, so 976 = P x (5/100)^2 x (305/100). So P = (976 x 1000000) / (25 x 305) = Rs 128000. Check: P x (R/100)^2 x (3+R/100) = 128000 x (5/100)^2 x (305/100) = Rs 976, matching the given difference.
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Q4. The difference between the compound interest and the simple interest on a certain sum for 3 years at 5% per annum is Rs 1708. Find the sum.
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Answer: B
Let the sum be P, Rate R = 5% per annum, Time = 3 years. For 3 years, the standard result is C.I. – S.I. = P x (R/100)^2 x (3 + R/100). Given C.I. – S.I. = Rs 1708, so 1708 = P x (5/100)^2 x (305/100). So P = (1708 x 1000000) / (25 x 305) = Rs 224000. Check: P x (R/100)^2 x (3+R/100) = 224000 x (5/100)^2 x (305/100) = Rs 1708, matching the given difference.
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Q5. The difference between the compound interest and the simple interest on a certain sum for 2 years at 5% per annum is Rs 4. Find the sum.
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Answer: D
Let the sum be P, Rate R = 5% per annum, Time = 2 years. S.I. earns the same interest each year. C.I. also earns interest on year 1’s interest, during year 2. So for 2 years, C.I. – S.I. = P x (R/100)^2. Given C.I. – S.I. = Rs 4, so 4 = P x (5/100)^2. So P = (4 x 10000) / 25 = Rs 1600. Check: P x (R/100)^2 = 1600 x (5/100)^2 = Rs 4, matching the given difference.
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Q6. The difference between the compound interest and the simple interest on a certain sum for 2 years at 25% per annum is Rs 725. Find the sum.
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Answer: A
Let the sum be P, Rate R = 25% per annum, Time = 2 years. S.I. earns the same interest each year. C.I. also earns interest on year 1’s interest, during year 2. So for 2 years, C.I. – S.I. = P x (R/100)^2. Given C.I. – S.I. = Rs 725, so 725 = P x (25/100)^2. So P = (725 x 10000) / 625 = Rs 11600. Check: P x (R/100)^2 = 11600 x (25/100)^2 = Rs 725, matching the given difference.
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Q7. The difference between the compound interest and the simple interest on a certain sum for 2 years at 25% per annum is Rs 1025. Find the sum.
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Answer: A
Let the sum be P, Rate R = 25% per annum, Time = 2 years. S.I. earns the same interest each year. C.I. also earns interest on year 1’s interest, during year 2. So for 2 years, C.I. – S.I. = P x (R/100)^2. Given C.I. – S.I. = Rs 1025, so 1025 = P x (25/100)^2. So P = (1025 x 10000) / 625 = Rs 16400. Check: P x (R/100)^2 = 16400 x (25/100)^2 = Rs 1025, matching the given difference.
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Q8. The difference between the compound interest and the simple interest on a certain sum for 2 years at 15% per annum is Rs 324. Find the sum.
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Answer: D
Let the sum be P, Rate R = 15% per annum, Time = 2 years. S.I. earns the same interest each year. C.I. also earns interest on year 1’s interest, during year 2. So for 2 years, C.I. – S.I. = P x (R/100)^2. Given C.I. – S.I. = Rs 324, so 324 = P x (15/100)^2. So P = (324 x 10000) / 225 = Rs 14400. Check: P x (R/100)^2 = 14400 x (15/100)^2 = Rs 324, matching the given difference.
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Q9. The difference between the compound interest and the simple interest on a certain sum for 2 years at 15% per annum is Rs 333. Find the sum.
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Answer: C
Let the sum be P, Rate R = 15% per annum, Time = 2 years. S.I. earns the same interest each year. C.I. also earns interest on year 1’s interest, during year 2. So for 2 years, C.I. – S.I. = P x (R/100)^2. Given C.I. – S.I. = Rs 333, so 333 = P x (15/100)^2. So P = (333 x 10000) / 225 = Rs 14800. Check: P x (R/100)^2 = 14800 x (15/100)^2 = Rs 333, matching the given difference.
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Q10. The difference between the compound interest and the simple interest on a certain sum for 2 years at 10% per annum is Rs 100. Find the sum.
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Answer: B
Let the sum be P, Rate R = 10% per annum, Time = 2 years. S.I. earns the same interest each year. C.I. also earns interest on year 1’s interest, during year 2. So for 2 years, C.I. – S.I. = P x (R/100)^2. Given C.I. – S.I. = Rs 100, so 100 = P x (10/100)^2. So P = (100 x 10000) / 100 = Rs 10000. Check: P x (R/100)^2 = 10000 x (10/100)^2 = Rs 100, matching the given difference.
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Q11. The difference between the compound interest and the simple interest on a certain sum for 2 years at 4% per annum is Rs 16. Find the sum.
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Answer: B
Let the sum be P, Rate R = 4% per annum, Time = 2 years. S.I. earns the same interest each year. C.I. also earns interest on year 1’s interest, during year 2. So for 2 years, C.I. – S.I. = P x (R/100)^2. Given C.I. – S.I. = Rs 16, so 16 = P x (4/100)^2. So P = (16 x 10000) / 16 = Rs 10000. Check: P x (R/100)^2 = 10000 x (4/100)^2 = Rs 16, matching the given difference.
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Q12. The difference between the compound interest and the simple interest on a certain sum for 2 years at 20% per annum is Rs 336. Find the sum.
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Answer: C
Let the sum be P, Rate R = 20% per annum, Time = 2 years. S.I. earns the same interest each year. C.I. also earns interest on year 1’s interest, during year 2. So for 2 years, C.I. – S.I. = P x (R/100)^2. Given C.I. – S.I. = Rs 336, so 336 = P x (20/100)^2. So P = (336 x 10000) / 400 = Rs 8400. Check: P x (R/100)^2 = 8400 x (20/100)^2 = Rs 336, matching the given difference.
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Q13. The difference between the compound interest and the simple interest on a certain sum for 2 years at 15% per annum is Rs 531. Find the sum.
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Answer: D
Let the sum be P, Rate R = 15% per annum, Time = 2 years. S.I. earns the same interest each year. C.I. also earns interest on year 1’s interest, during year 2. So for 2 years, C.I. – S.I. = P x (R/100)^2. Given C.I. – S.I. = Rs 531, so 531 = P x (15/100)^2. So P = (531 x 10000) / 225 = Rs 23600. Check: P x (R/100)^2 = 23600 x (15/100)^2 = Rs 531, matching the given difference.
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Q14. The difference between the compound interest and the simple interest on a certain sum for 2 years at 15% per annum is Rs 306. Find the sum.
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Answer: A
Let the sum be P, Rate R = 15% per annum, Time = 2 years. S.I. earns the same interest each year. C.I. also earns interest on year 1’s interest, during year 2. So for 2 years, C.I. – S.I. = P x (R/100)^2. Given C.I. – S.I. = Rs 306, so 306 = P x (15/100)^2. So P = (306 x 10000) / 225 = Rs 13600. Check: P x (R/100)^2 = 13600 x (15/100)^2 = Rs 306, matching the given difference.
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Q15. The difference between the compound interest and the simple interest on a certain sum for 2 years at 40% per annum is Rs 3072. Find the sum.
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Answer: D
Let the sum be P, Rate R = 40% per annum, Time = 2 years. S.I. earns the same interest each year. C.I. also earns interest on year 1’s interest, during year 2. So for 2 years, C.I. – S.I. = P x (R/100)^2. Given C.I. – S.I. = Rs 3072, so 3072 = P x (40/100)^2. So P = (3072 x 10000) / 1600 = Rs 19200. Check: P x (R/100)^2 = 19200 x (40/100)^2 = Rs 3072, matching the given difference.
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Q16. The difference between the compound interest and the simple interest on a certain sum for 2 years at 5% per annum is Rs 47. Find the sum.
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Answer: A
Let the sum be P, Rate R = 5% per annum, Time = 2 years. S.I. earns the same interest each year. C.I. also earns interest on year 1’s interest, during year 2. So for 2 years, C.I. – S.I. = P x (R/100)^2. Given C.I. – S.I. = Rs 47, so 47 = P x (5/100)^2. So P = (47 x 10000) / 25 = Rs 18800. Check: P x (R/100)^2 = 18800 x (5/100)^2 = Rs 47, matching the given difference.
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Q17. Find the compound interest on Rs 1562500 at 16% per annum for 1 year, interest being compounded quarterly.
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Answer: C
Let Principal P = Rs 1562500, Rate R = 16% per annum, Time T = 1 year. Compounding is quarterly, so divide the rate by 4 and multiply the periods by 4. Quarterly rate = R/4 = 16/4 = 4%. Number of quarters = 4 x T = 4 x 1 = 4. After quarter 1, Amount = 1562500 x 26/25 = Rs 1625000. After quarter 2, Amount = 1625000 x 26/25 = Rs 1690000. After quarter 3, Amount = 1690000 x 26/25 = Rs 1757600. After quarter 4, Amount = 1757600 x 26/25 = Rs 1827904. So Amount after 4 quarters = Rs 1827904. C.I. = Amount – Principal = 1827904 – 1562500 = Rs 265404. Check: Principal + C.I. = 1562500 + 265404 = Rs 1827904, which matches the Amount.
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Q18. Find the compound interest on Rs 160000 at 20% per annum for 1 year, interest being compounded quarterly.
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Answer: B
Let Principal P = Rs 160000, Rate R = 20% per annum, Time T = 1 year. Compounding is quarterly, so divide the rate by 4 and multiply the periods by 4. Quarterly rate = R/4 = 20/4 = 5%. Number of quarters = 4 x T = 4 x 1 = 4. After quarter 1, Amount = 160000 x 21/20 = Rs 168000. After quarter 2, Amount = 168000 x 21/20 = Rs 176400. After quarter 3, Amount = 176400 x 21/20 = Rs 185220. After quarter 4, Amount = 185220 x 21/20 = Rs 194481. So Amount after 4 quarters = Rs 194481. C.I. = Amount – Principal = 194481 – 160000 = Rs 34481. Check: Principal + C.I. = 160000 + 34481 = Rs 194481, which matches the Amount.
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Q19. Find the compound interest on Rs 800000 at 20% per annum for 1 year, interest being compounded quarterly.
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Answer: C
Let Principal P = Rs 800000, Rate R = 20% per annum, Time T = 1 year. Compounding is quarterly, so divide the rate by 4 and multiply the periods by 4. Quarterly rate = R/4 = 20/4 = 5%. Number of quarters = 4 x T = 4 x 1 = 4. After quarter 1, Amount = 800000 x 21/20 = Rs 840000. After quarter 2, Amount = 840000 x 21/20 = Rs 882000. After quarter 3, Amount = 882000 x 21/20 = Rs 926100. After quarter 4, Amount = 926100 x 21/20 = Rs 972405. So Amount after 4 quarters = Rs 972405. C.I. = Amount – Principal = 972405 – 800000 = Rs 172405. Check: Principal + C.I. = 800000 + 172405 = Rs 972405, which matches the Amount.
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Q20. Find the compound interest on Rs 1120000 at 20% per annum for 1 year, interest being compounded quarterly.
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Answer: A
Let Principal P = Rs 1120000, Rate R = 20% per annum, Time T = 1 year. Compounding is quarterly, so divide the rate by 4 and multiply the periods by 4. Quarterly rate = R/4 = 20/4 = 5%. Number of quarters = 4 x T = 4 x 1 = 4. After quarter 1, Amount = 1120000 x 21/20 = Rs 1176000. After quarter 2, Amount = 1176000 x 21/20 = Rs 1234800. After quarter 3, Amount = 1234800 x 21/20 = Rs 1296540. After quarter 4, Amount = 1296540 x 21/20 = Rs 1361367. So Amount after 4 quarters = Rs 1361367. C.I. = Amount – Principal = 1361367 – 1120000 = Rs 241367. Check: Principal + C.I. = 1120000 + 241367 = Rs 1361367, which matches the Amount.
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Q21. Find the compound interest on Rs 90000 at 40% per annum for 1 year, interest being compounded quarterly.
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Answer: B
Let Principal P = Rs 90000, Rate R = 40% per annum, Time T = 1 year. Compounding is quarterly, so divide the rate by 4 and multiply the periods by 4. Quarterly rate = R/4 = 40/4 = 10%. Number of quarters = 4 x T = 4 x 1 = 4. After quarter 1, Amount = 90000 x 11/10 = Rs 99000. After quarter 2, Amount = 99000 x 11/10 = Rs 108900. After quarter 3, Amount = 108900 x 11/10 = Rs 119790. After quarter 4, Amount = 119790 x 11/10 = Rs 131769. So Amount after 4 quarters = Rs 131769. C.I. = Amount – Principal = 131769 – 90000 = Rs 41769. Check: Principal + C.I. = 90000 + 41769 = Rs 131769, which matches the Amount.
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Q22. Find the compound interest on Rs 40000 at 40% per annum for 1 year, interest being compounded quarterly.
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Answer: D
Let Principal P = Rs 40000, Rate R = 40% per annum, Time T = 1 year. Compounding is quarterly, so divide the rate by 4 and multiply the periods by 4. Quarterly rate = R/4 = 40/4 = 10%. Number of quarters = 4 x T = 4 x 1 = 4. After quarter 1, Amount = 40000 x 11/10 = Rs 44000. After quarter 2, Amount = 44000 x 11/10 = Rs 48400. After quarter 3, Amount = 48400 x 11/10 = Rs 53240. After quarter 4, Amount = 53240 x 11/10 = Rs 58564. So Amount after 4 quarters = Rs 58564. C.I. = Amount – Principal = 58564 – 40000 = Rs 18564. Check: Principal + C.I. = 40000 + 18564 = Rs 58564, which matches the Amount.
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Q23. Find the compound interest on Rs 1171875 at 16% per annum for 1 year, interest being compounded quarterly.
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Answer: A
Let Principal P = Rs 1171875, Rate R = 16% per annum, Time T = 1 year. Compounding is quarterly, so divide the rate by 4 and multiply the periods by 4. Quarterly rate = R/4 = 16/4 = 4%. Number of quarters = 4 x T = 4 x 1 = 4. After quarter 1, Amount = 1171875 x 26/25 = Rs 1218750. After quarter 2, Amount = 1218750 x 26/25 = Rs 1267500. After quarter 3, Amount = 1267500 x 26/25 = Rs 1318200. After quarter 4, Amount = 1318200 x 26/25 = Rs 1370928. So Amount after 4 quarters = Rs 1370928. C.I. = Amount – Principal = 1370928 – 1171875 = Rs 199053. Check: Principal + C.I. = 1171875 + 199053 = Rs 1370928, which matches the Amount.
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Q24. Find the compound interest on Rs 3125000 at 16% per annum for 1 year, interest being compounded quarterly.
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Answer: C
Let Principal P = Rs 3125000, Rate R = 16% per annum, Time T = 1 year. Compounding is quarterly, so divide the rate by 4 and multiply the periods by 4. Quarterly rate = R/4 = 16/4 = 4%. Number of quarters = 4 x T = 4 x 1 = 4. After quarter 1, Amount = 3125000 x 26/25 = Rs 3250000. After quarter 2, Amount = 3250000 x 26/25 = Rs 3380000. After quarter 3, Amount = 3380000 x 26/25 = Rs 3515200. After quarter 4, Amount = 3515200 x 26/25 = Rs 3655808. So Amount after 4 quarters = Rs 3655808. C.I. = Amount – Principal = 3655808 – 3125000 = Rs 530808. Check: Principal + C.I. = 3125000 + 530808 = Rs 3655808, which matches the Amount.
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Q25. Find the compound interest on Rs 640000 at 20% per annum for 1 year, interest being compounded quarterly.
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Answer: B
Let Principal P = Rs 640000, Rate R = 20% per annum, Time T = 1 year. Compounding is quarterly, so divide the rate by 4 and multiply the periods by 4. Quarterly rate = R/4 = 20/4 = 5%. Number of quarters = 4 x T = 4 x 1 = 4. After quarter 1, Amount = 640000 x 21/20 = Rs 672000. After quarter 2, Amount = 672000 x 21/20 = Rs 705600. After quarter 3, Amount = 705600 x 21/20 = Rs 740880. After quarter 4, Amount = 740880 x 21/20 = Rs 777924. So Amount after 4 quarters = Rs 777924. C.I. = Amount – Principal = 777924 – 640000 = Rs 137924. Check: Principal + C.I. = 640000 + 137924 = Rs 777924, which matches the Amount.
Related topics: Compound Interest: Formulas, Shortcuts and Solved Examples