Compound Interest: Formulas, Shortcuts and Solved Examples — MCQs with Answers (Set 4)

Let Principal P = Rs 960000, 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 = 960000 x 21/20 = Rs 1008000. After quarter 2, Amount = 1008000 x 21/20 = Rs 1058400. After quarter 3, Amount = 1058400 x 21/20 = Rs 1111320. After quarter 4, Amount = 1111320 x 21/20 = Rs 1166886. So Amount after 4 quarters = Rs 1166886. C.I. = Amount – Principal = 1166886 – 960000 = Rs 206886. Check: Principal + C.I. = 960000 + 206886 = Rs 1166886, which matches the Amount.

Let Principal P = Rs 4400, Rate R = 10% per annum, Time T = 1 year. Compounding is half-yearly, so halve the rate and double the number of periods. Half-year rate = R/2 = 10/2 = 5%. Number of half-year periods = 2 x T = 2 x 1 = 2. After half-year 1, Amount = 4400 x 21/20 = Rs 4620. After half-year 2, Amount = 4620 x 21/20 = Rs 4851. So Amount after 2 half-years = Rs 4851. C.I. = Amount – Principal = 4851 – 4400 = Rs 451. Check: Principal + C.I. = 4400 + 451 = Rs 4851, which matches the Amount.

Let Principal P = Rs 3125, Rate R = 16% per annum, Time T = 1 year. Compounding is half-yearly, so halve the rate and double the number of periods. Half-year rate = R/2 = 16/2 = 8%. Number of half-year periods = 2 x T = 2 x 1 = 2. After half-year 1, Amount = 3125 x 27/25 = Rs 3375. After half-year 2, Amount = 3375 x 27/25 = Rs 3645. So Amount after 2 half-years = Rs 3645. C.I. = Amount – Principal = 3645 – 3125 = Rs 520. Check: Principal + C.I. = 3125 + 520 = Rs 3645, which matches the Amount.

Let Principal P = Rs 325, Rate R = 40% per annum, Time T = 1 year. Compounding is half-yearly, so halve the rate and double the number of periods. Half-year rate = R/2 = 40/2 = 20%. Number of half-year periods = 2 x T = 2 x 1 = 2. After half-year 1, Amount = 325 x 6/5 = Rs 390. After half-year 2, Amount = 390 x 6/5 = Rs 468. So Amount after 2 half-years = Rs 468. C.I. = Amount – Principal = 468 – 325 = Rs 143. Check: Principal + C.I. = 325 + 143 = Rs 468, which matches the Amount.

Let Principal P = Rs 70000, Rate R = 20% per annum, Time T = 2 years. Compounding is half-yearly, so halve the rate and double the number of periods. Half-year rate = R/2 = 20/2 = 10%. Number of half-year periods = 2 x T = 2 x 2 = 4. After half-year 1, Amount = 70000 x 11/10 = Rs 77000. After half-year 2, Amount = 77000 x 11/10 = Rs 84700. After half-year 3, Amount = 84700 x 11/10 = Rs 93170. After half-year 4, Amount = 93170 x 11/10 = Rs 102487. So Amount after 4 half-years = Rs 102487. C.I. = Amount – Principal = 102487 – 70000 = Rs 32487. Check: Principal + C.I. = 70000 + 32487 = Rs 102487, which matches the Amount.

Let Principal P = Rs 60000, Rate R = 20% per annum, Time T = 2 years. Compounding is half-yearly, so halve the rate and double the number of periods. Half-year rate = R/2 = 20/2 = 10%. Number of half-year periods = 2 x T = 2 x 2 = 4. After half-year 1, Amount = 60000 x 11/10 = Rs 66000. After half-year 2, Amount = 66000 x 11/10 = Rs 72600. After half-year 3, Amount = 72600 x 11/10 = Rs 79860. After half-year 4, Amount = 79860 x 11/10 = Rs 87846. So Amount after 4 half-years = Rs 87846. C.I. = Amount – Principal = 87846 – 60000 = Rs 27846. Check: Principal + C.I. = 60000 + 27846 = Rs 87846, which matches the Amount.

Let Principal P = Rs 5000, Rate R = 16% per annum, Time T = 1 year. Compounding is half-yearly, so halve the rate and double the number of periods. Half-year rate = R/2 = 16/2 = 8%. Number of half-year periods = 2 x T = 2 x 1 = 2. After half-year 1, Amount = 5000 x 27/25 = Rs 5400. After half-year 2, Amount = 5400 x 27/25 = Rs 5832. So Amount after 2 half-years = Rs 5832. C.I. = Amount – Principal = 5832 – 5000 = Rs 832. Check: Principal + C.I. = 5000 + 832 = Rs 5832, which matches the Amount.

Let Principal P = Rs 4375, Rate R = 8% per annum, Time T = 1 year. Compounding is half-yearly, so halve the rate and double the number of periods. Half-year rate = R/2 = 8/2 = 4%. Number of half-year periods = 2 x T = 2 x 1 = 2. After half-year 1, Amount = 4375 x 26/25 = Rs 4550. After half-year 2, Amount = 4550 x 26/25 = Rs 4732. So Amount after 2 half-years = Rs 4732. C.I. = Amount – Principal = 4732 – 4375 = Rs 357. Check: Principal + C.I. = 4375 + 357 = Rs 4732, which matches the Amount.

Let Principal P = Rs 3125000, Rate R = 16% per annum, Time T = 2 years. Compounding is half-yearly, so halve the rate and double the number of periods. Half-year rate = R/2 = 16/2 = 8%. Number of half-year periods = 2 x T = 2 x 2 = 4. After half-year 1, Amount = 3125000 x 27/25 = Rs 3375000. After half-year 2, Amount = 3375000 x 27/25 = Rs 3645000. After half-year 3, Amount = 3645000 x 27/25 = Rs 3936600. After half-year 4, Amount = 3936600 x 27/25 = Rs 4251528. So Amount after 4 half-years = Rs 4251528. C.I. = Amount – Principal = 4251528 – 3125000 = Rs 1126528. Check: Principal + C.I. = 3125000 + 1126528 = Rs 4251528, which matches the Amount.

Let Principal P = Rs 1500, Rate R = 20% per annum, Time T = 1 year. Compounding is half-yearly, so halve the rate and double the number of periods. Half-year rate = R/2 = 20/2 = 10%. Number of half-year periods = 2 x T = 2 x 1 = 2. After half-year 1, Amount = 1500 x 11/10 = Rs 1650. After half-year 2, Amount = 1650 x 11/10 = Rs 1815. So Amount after 2 half-years = Rs 1815. C.I. = Amount – Principal = 1815 – 1500 = Rs 315. Check: Principal + C.I. = 1500 + 315 = Rs 1815, which matches the Amount.

Let Principal P = Rs 3840, Rate R = 50% per annum, Time T = 2 years. Compounding is half-yearly, so halve the rate and double the number of periods. Half-year rate = R/2 = 50/2 = 25%. Number of half-year periods = 2 x T = 2 x 2 = 4. After half-year 1, Amount = 3840 x 5/4 = Rs 4800. After half-year 2, Amount = 4800 x 5/4 = Rs 6000. After half-year 3, Amount = 6000 x 5/4 = Rs 7500. After half-year 4, Amount = 7500 x 5/4 = Rs 9375. So Amount after 4 half-years = Rs 9375. C.I. = Amount – Principal = 9375 – 3840 = Rs 5535. Check: Principal + C.I. = 3840 + 5535 = Rs 9375, which matches the Amount.

Let Principal P = Rs 1440000, Rate R = 10% per annum, Time T = 2 years. Compounding is half-yearly, so halve the rate and double the number of periods. Half-year rate = R/2 = 10/2 = 5%. Number of half-year periods = 2 x T = 2 x 2 = 4. After half-year 1, Amount = 1440000 x 21/20 = Rs 1512000. After half-year 2, Amount = 1512000 x 21/20 = Rs 1587600. After half-year 3, Amount = 1587600 x 21/20 = Rs 1666980. After half-year 4, Amount = 1666980 x 21/20 = Rs 1750329. So Amount after 4 half-years = Rs 1750329. C.I. = Amount – Principal = 1750329 – 1440000 = Rs 310329. Check: Principal + C.I. = 1440000 + 310329 = Rs 1750329, which matches the Amount.

Let Principal P = Rs 6875, Rate R = 16% per annum, Time T = 1 year. Compounding is half-yearly, so halve the rate and double the number of periods. Half-year rate = R/2 = 16/2 = 8%. Number of half-year periods = 2 x T = 2 x 1 = 2. After half-year 1, Amount = 6875 x 27/25 = Rs 7425. After half-year 2, Amount = 7425 x 27/25 = Rs 8019. So Amount after 2 half-years = Rs 8019. C.I. = Amount – Principal = 8019 – 6875 = Rs 1144. Check: Principal + C.I. = 6875 + 1144 = Rs 8019, which matches the Amount.

Let Principal P = Rs 1625, Rate R = 20% per annum, Time T = 3 years. Compounded annually, the formula is Amount = P(1+R/100)^T = P x (6/5)^T. After year 1, Amount = 1625 x 6/5 = Rs 1950. After year 2, Amount = 1950 x 6/5 = Rs 2340. After year 3, Amount = 2340 x 6/5 = Rs 2808. So Amount after 3 years = Rs 2808. Check: Interest earned = 2808 – 1625 = Rs 1183, consistent with growth at 20% per annum.

Let Principal P = Rs 256, Rate R = 25% per annum, Time T = 2 years. Compounded annually, the formula is Amount = P(1+R/100)^T = P x (5/4)^T. After year 1, Amount = 256 x 5/4 = Rs 320. After year 2, Amount = 320 x 5/4 = Rs 400. So Amount after 2 years = Rs 400. Check: Interest earned = 400 – 256 = Rs 144, consistent with growth at 25% per annum.

Let Principal P = Rs 576, Rate R = 25% per annum, Time T = 3 years. Compounded annually, the formula is Amount = P(1+R/100)^T = P x (5/4)^T. After year 1, Amount = 576 x 5/4 = Rs 720. After year 2, Amount = 720 x 5/4 = Rs 900. After year 3, Amount = 900 x 5/4 = Rs 1125. So Amount after 3 years = Rs 1125. Check: Interest earned = 1125 – 576 = Rs 549, consistent with growth at 25% per annum.

Let Principal P = Rs 400, Rate R = 20% per annum, Time T = 2 years. Compounded annually, the formula is Amount = P(1+R/100)^T = P x (6/5)^T. After year 1, Amount = 400 x 6/5 = Rs 480. After year 2, Amount = 480 x 6/5 = Rs 576. So Amount after 2 years = Rs 576. Check: Interest earned = 576 – 400 = Rs 176, consistent with growth at 20% per annum.

Let Principal P = Rs 2500, Rate R = 8% per annum, Time T = 2 years. Compounded annually, the formula is Amount = P(1+R/100)^T = P x (27/25)^T. After year 1, Amount = 2500 x 27/25 = Rs 2700. After year 2, Amount = 2700 x 27/25 = Rs 2916. So Amount after 2 years = Rs 2916. Check: Interest earned = 2916 – 2500 = Rs 416, consistent with growth at 8% per annum.

Let Principal P = Rs 1875, Rate R = 20% per annum, Time T = 3 years. Compounded annually, the formula is Amount = P(1+R/100)^T = P x (6/5)^T. After year 1, Amount = 1875 x 6/5 = Rs 2250. After year 2, Amount = 2250 x 6/5 = Rs 2700. After year 3, Amount = 2700 x 6/5 = Rs 3240. So Amount after 3 years = Rs 3240. Check: Interest earned = 3240 – 1875 = Rs 1365, consistent with growth at 20% per annum.

Let Principal P = Rs 1216, Rate R = 25% per annum, Time T = 3 years. Compounded annually, the formula is Amount = P(1+R/100)^T = P x (5/4)^T. After year 1, Amount = 1216 x 5/4 = Rs 1520. After year 2, Amount = 1520 x 5/4 = Rs 1900. After year 3, Amount = 1900 x 5/4 = Rs 2375. So Amount after 3 years = Rs 2375. Check: Interest earned = 2375 – 1216 = Rs 1159, consistent with growth at 25% per annum.

Let Principal P = Rs 12500, Rate R = 4% per annum, Time T = 2 years. Compounded annually, the formula is Amount = P(1+R/100)^T = P x (26/25)^T. After year 1, Amount = 12500 x 26/25 = Rs 13000. After year 2, Amount = 13000 x 26/25 = Rs 13520. So Amount after 2 years = Rs 13520. Check: Interest earned = 13520 – 12500 = Rs 1020, consistent with growth at 4% per annum.

Let Principal P = Rs 64, Rate R = 25% per annum, Time T = 3 years. Compounded annually, the formula is Amount = P(1+R/100)^T = P x (5/4)^T. After year 1, Amount = 64 x 5/4 = Rs 80. After year 2, Amount = 80 x 5/4 = Rs 100. After year 3, Amount = 100 x 5/4 = Rs 125. So Amount after 3 years = Rs 125. Check: Interest earned = 125 – 64 = Rs 61, consistent with growth at 25% per annum.

Let Principal P = Rs 32, Rate R = 50% per annum, Time T = 2 years. Compounded annually, the formula is Amount = P(1+R/100)^T = P x (3/2)^T. After year 1, Amount = 32 x 3/2 = Rs 48. After year 2, Amount = 48 x 3/2 = Rs 72. So Amount after 2 years = Rs 72. Check: Interest earned = 72 – 32 = Rs 40, consistent with growth at 50% per annum.

Let Principal P = Rs 2400, Rate R = 5% per annum, Time T = 2 years. Compounded annually, the formula is Amount = P(1+R/100)^T = P x (21/20)^T. After year 1, Amount = 2400 x 21/20 = Rs 2520. After year 2, Amount = 2520 x 21/20 = Rs 2646. So Amount after 2 years = Rs 2646. Check: Interest earned = 2646 – 2400 = Rs 246, consistent with growth at 5% per annum.

Let Principal P = Rs 8750, Rate R = 12% per annum, Time T = 2 years. Compounded annually, the formula is Amount = P(1+R/100)^T = P x (28/25)^T. After year 1, Amount = 8750 x 28/25 = Rs 9800. After year 2, Amount = 9800 x 28/25 = Rs 10976. So Amount after 2 years = Rs 10976. Check: Interest earned = 10976 – 8750 = Rs 2226, consistent with growth at 12% per annum.

Let Principal P = Rs 3125, Rate R = 4% per annum, Time T = 2 years. Compounded annually, each year the amount is multiplied by (100+R)/100 = 26/25. After year 1, Amount = 3125 x 26/25 = Rs 3250. After year 2, Amount = 3250 x 26/25 = Rs 3380. So Amount after 2 years = Rs 3380. C.I. = Amount – Principal = 3380 – 3125 = Rs 255. Check: Principal + C.I. = 3125 + 255 = Rs 3380, which matches the Amount.

Let Principal P = Rs 6875, Rate R = 12% per annum, Time T = 2 years. Compounded annually, each year the amount is multiplied by (100+R)/100 = 28/25. After year 1, Amount = 6875 x 28/25 = Rs 7700. After year 2, Amount = 7700 x 28/25 = Rs 8624. So Amount after 2 years = Rs 8624. C.I. = Amount – Principal = 8624 – 6875 = Rs 1749. Check: Principal + C.I. = 6875 + 1749 = Rs 8624, which matches the Amount.

Let Principal P = Rs 1375, Rate R = 40% per annum, Time T = 3 years. Compounded annually, each year the amount is multiplied by (100+R)/100 = 7/5. After year 1, Amount = 1375 x 7/5 = Rs 1925. After year 2, Amount = 1925 x 7/5 = Rs 2695. After year 3, Amount = 2695 x 7/5 = Rs 3773. So Amount after 3 years = Rs 3773. C.I. = Amount – Principal = 3773 – 1375 = Rs 2398. Check: Principal + C.I. = 1375 + 2398 = Rs 3773, which matches the Amount.

Let Principal P = Rs 109375, Rate R = 12% per annum, Time T = 3 years. Compounded annually, each year the amount is multiplied by (100+R)/100 = 28/25. After year 1, Amount = 109375 x 28/25 = Rs 122500. After year 2, Amount = 122500 x 28/25 = Rs 137200. After year 3, Amount = 137200 x 28/25 = Rs 153664. So Amount after 3 years = Rs 153664. C.I. = Amount – Principal = 153664 – 109375 = Rs 44289. Check: Principal + C.I. = 109375 + 44289 = Rs 153664, which matches the Amount.

Let Principal P = Rs 8125, Rate R = 8% per annum, Time T = 2 years. Compounded annually, each year the amount is multiplied by (100+R)/100 = 27/25. After year 1, Amount = 8125 x 27/25 = Rs 8775. After year 2, Amount = 8775 x 27/25 = Rs 9477. So Amount after 2 years = Rs 9477. C.I. = Amount – Principal = 9477 – 8125 = Rs 1352. Check: Principal + C.I. = 8125 + 1352 = Rs 9477, which matches the Amount.

Let Principal P = Rs 8750, Rate R = 8% per annum, Time T = 2 years. Compounded annually, each year the amount is multiplied by (100+R)/100 = 27/25. After year 1, Amount = 8750 x 27/25 = Rs 9450. After year 2, Amount = 9450 x 27/25 = Rs 10206. So Amount after 2 years = Rs 10206. C.I. = Amount – Principal = 10206 – 8750 = Rs 1456. Check: Principal + C.I. = 8750 + 1456 = Rs 10206, which matches the Amount.

Let Principal P = Rs 1000, Rate R = 40% per annum, Time T = 3 years. Compounded annually, each year the amount is multiplied by (100+R)/100 = 7/5. After year 1, Amount = 1000 x 7/5 = Rs 1400. After year 2, Amount = 1400 x 7/5 = Rs 1960. After year 3, Amount = 1960 x 7/5 = Rs 2744. So Amount after 3 years = Rs 2744. C.I. = Amount – Principal = 2744 – 1000 = Rs 1744. Check: Principal + C.I. = 1000 + 1744 = Rs 2744, which matches the Amount.

Let Principal P = Rs 2125, Rate R = 40% per annum, Time T = 3 years. Compounded annually, each year the amount is multiplied by (100+R)/100 = 7/5. After year 1, Amount = 2125 x 7/5 = Rs 2975. After year 2, Amount = 2975 x 7/5 = Rs 4165. After year 3, Amount = 4165 x 7/5 = Rs 5831. So Amount after 3 years = Rs 5831. C.I. = Amount – Principal = 5831 – 2125 = Rs 3706. Check: Principal + C.I. = 2125 + 3706 = Rs 5831, which matches the Amount.

Let Principal P = Rs 156250, Rate R = 16% per annum, Time T = 3 years. Compounded annually, each year the amount is multiplied by (100+R)/100 = 29/25. After year 1, Amount = 156250 x 29/25 = Rs 181250. After year 2, Amount = 181250 x 29/25 = Rs 210250. After year 3, Amount = 210250 x 29/25 = Rs 243890. So Amount after 3 years = Rs 243890. C.I. = Amount – Principal = 243890 – 156250 = Rs 87640. Check: Principal + C.I. = 156250 + 87640 = Rs 243890, which matches the Amount.

Let Principal P = Rs 100, Rate R = 40% per annum, Time T = 2 years. Compounded annually, each year the amount is multiplied by (100+R)/100 = 7/5. After year 1, Amount = 100 x 7/5 = Rs 140. After year 2, Amount = 140 x 7/5 = Rs 196. So Amount after 2 years = Rs 196. C.I. = Amount – Principal = 196 – 100 = Rs 96. Check: Principal + C.I. = 100 + 96 = Rs 196, which matches the Amount.

Let Principal P = Rs 3000, Rate R = 10% per annum, Time T = 3 years. Compounded annually, each year the amount is multiplied by (100+R)/100 = 11/10. After year 1, Amount = 3000 x 11/10 = Rs 3300. After year 2, Amount = 3300 x 11/10 = Rs 3630. After year 3, Amount = 3630 x 11/10 = Rs 3993. So Amount after 3 years = Rs 3993. C.I. = Amount – Principal = 3993 – 3000 = Rs 993. Check: Principal + C.I. = 3000 + 993 = Rs 3993, which matches the Amount.

Let Principal P = Rs 62500, Rate R = 4% per annum, Time T = 3 years. Compounded annually, each year the amount is multiplied by (100+R)/100 = 26/25. After year 1, Amount = 62500 x 26/25 = Rs 65000. After year 2, Amount = 65000 x 26/25 = Rs 67600. After year 3, Amount = 67600 x 26/25 = Rs 70304. So Amount after 3 years = Rs 70304. C.I. = Amount – Principal = 70304 – 62500 = Rs 7804. Check: Principal + C.I. = 62500 + 7804 = Rs 70304, which matches the Amount.

Let Principal P = Rs 11875, Rate R = 4% per annum, Time T = 2 years. Compounded annually, each year the amount is multiplied by (100+R)/100 = 26/25. After year 1, Amount = 11875 x 26/25 = Rs 12350. After year 2, Amount = 12350 x 26/25 = Rs 12844. So Amount after 2 years = Rs 12844. C.I. = Amount – Principal = 12844 – 11875 = Rs 969. Check: Principal + C.I. = 11875 + 969 = Rs 12844, which matches the Amount.

Let Principal P = Rs 1500, Rate R = 40% per annum, Time T = 3 years. Compounded annually, each year the amount is multiplied by (100+R)/100 = 7/5. After year 1, Amount = 1500 x 7/5 = Rs 2100. After year 2, Amount = 2100 x 7/5 = Rs 2940. After year 3, Amount = 2940 x 7/5 = Rs 4116. So Amount after 3 years = Rs 4116. C.I. = Amount – Principal = 4116 – 1500 = Rs 2616. Check: Principal + C.I. = 1500 + 2616 = Rs 4116, which matches the Amount.

Let Principal P = Rs 234375, Rate R = 4% per annum, Time T = 3 years. Compounded annually, each year the amount is multiplied by (100+R)/100 = 26/25. After year 1, Amount = 234375 x 26/25 = Rs 243750. After year 2, Amount = 243750 x 26/25 = Rs 253500. After year 3, Amount = 253500 x 26/25 = Rs 263640. So Amount after 3 years = Rs 263640. C.I. = Amount – Principal = 263640 – 234375 = Rs 29265. Check: Principal + C.I. = 234375 + 29265 = Rs 263640, which matches the Amount.

Let Principal P = Rs 112000, Rate R = 5% per annum, Time T = 3 years. Compounded annually, each year the amount is multiplied by (100+R)/100 = 21/20. After year 1, Amount = 112000 x 21/20 = Rs 117600. After year 2, Amount = 117600 x 21/20 = Rs 123480. After year 3, Amount = 123480 x 21/20 = Rs 129654. So Amount after 3 years = Rs 129654. C.I. = Amount – Principal = 129654 – 112000 = Rs 17654. Check: Principal + C.I. = 112000 + 17654 = Rs 129654, which matches the Amount.