Simple and compound interest
- At what rate of simple interest per annum will a sum of money double itself in 8 years? Answer: B. 12.5% Answer: (B) 12.5% To double, SI = P. P = P × R × 8/100 ⇒ R = 100/8 = 12.5% . 1
- What is the compound interest on ₹15,625 for 3 years at 8% per annum, compounded annually? Answer: C. ₹4,058 Answer: (C) ₹4,058 Amount = 15625 × (27/25)³ = 15625 × 19683/15625 = 19683 . CI = 19683 - 15625 = 4058 . (₹3,750 is the si... 1
- A sum of money amounts to ₹6,900 in 3 years and to ₹7,500 in 5 years at simple interest. What is the rate of interest per annum? Answer: D. 5% Answer: (D) 5% Interest for 2 years = 7500 - 6900 = 600, so 300 per year. Principal = 6900 - 3 × 300 = 6000 . Rate = 300/6000... 1
- What is the difference between the compound interest (compounded annually) and the simple interest on ₹12,000 for 2 years at 10% per annum? Answer: A. ₹120 Answer: (A) ₹120 For 2 years, CI - SI = P(R/100)² = 12000 × 0.01 = 120 . Check: CI = 2520, SI = 2400. 1
- A sum of money lent at simple interest amounts to Rs. 7,800 in 3 years and to Rs. 9,000 in 5 years. What is the rate of interest per annum? Answer: B. 10% Answer: (B) 10% Interest for 2 years = 9000 − 7800 = 1200, so Rs. 600 per year. Principal = 7800 − 3 × 600 = 6000. Rate = 600... 1
- What is the compound interest on Rs. 16,000 at 10% per annum for 3 years, compounded annually (in Rs.)? Answer: C. 5296 Answer: (C) 5296 Amount = 16000 × (1.1)³ = 21296 . CI = 21296 − 16000 = Rs. 5,296. 1
- What is the simple interest on Rs. 6,000 at 8% per annum for 3 years (in Rs.)? Answer: B. 1440 Answer: (B) 1440 SI = 6000 × 8 × 3/100 = 1440 . 1
- The difference between the compound interest (compounded annually) and the simple interest on a sum for 2 years at 10% per annum is Rs. 75. What is the sum (in Rs.)? Answer: C. 7500 Answer: (C) 7500 For 2 years, CI − SI = P(R/100)² . So 75 = P × 0.01 , P = Rs. 7,500. 1
- What amount will ₹8,000 become in 2 years at 5% per annum compound interest? Answer: A. ₹8820 Answer: (A) ₹8820 5% for 2 years = 10.25% effective. Amount = 8000 × 1.1025 = ₹8820. 1
- What is the difference between the compound interest and the simple interest on ₹5,000 for 2 years at 4% per annum? Answer: D. ₹8 Answer: (D) ₹8 Shortcut: for 2 years, CI − SI = P(R/100)² = 5000 × 16/10000 = ₹8. 1
- The simple interest on ₹4,500 for 4 years is ₹1,440. What is the rate of interest per annum? Answer: A. 8% Answer: (A) 8% R = SI × 100/P × T = 1440 × 100/4500 × 4 = 8% . 1
- At simple interest, a sum becomes three times itself in 10 years. What is the rate of interest per annum? Answer: B. 20% Answer: (B) 20% Three times means the interest is 2 × P, i.e. 200% in 10 years. Rate = 200 ÷ 10 = 20%. Trap: 30% uses 300% in... 1
- A sum at simple interest amounts to ₹9,800 in 5 years and to ₹12,005 in 8 years. What is the rate of interest per annum? Answer: D. 12% Answer: (D) 12% Interest for 3 years = 12,005 − 9,800 = ₹2205, so 1 year's interest = ₹735. Principal = 9,800 − 5 × 735 = ₹61... 1
- What is the compound interest on ₹16,000 for 1 year at 10% per annum, compounded half-yearly? Answer: B. ₹1640 Answer: (B) ₹1640 Half-yearly: rate = 5% per half-year, 2 periods. Effective = 5 + 5 + 0.25 = 10.25%. CI = 10.25% of 16,000... 1
- A sum of money doubles itself in 6 years at compound interest. In how many years will it become 8 times itself? Answer: A. 18 years Answer: (A) 18 years 8 = 2³, so it needs three doubling periods: 3 × 6 = 18 years. Trap: 42 years is what you get by tre... 1
- The difference between the compound interest and the simple interest on a sum for 3 years at 10% per annum is ₹93. What is the sum? Answer: C. ₹3000 Answer: (C) ₹3000 Shortcut: for 3 years, CI − SI = P(R/100)²(3 + R/100) = P × 0.01 × 3.1 = 0.031P . 0.031P = 93, so P = ₹30... 1
- The compound interest on a sum for 2 years at 5% per annum is ₹328. What is the sum? Answer: C. ₹3200 Answer: (C) ₹3200 5% for 2 years = 10.25% effective. 10.25% of P = 328, so P = 328 ÷ 0.1025 = ₹3200. 1
- A sum at compound interest amounts to ₹6,050 in 2 years and ₹6,655 in 3 years. What is the rate of interest per annum? Answer: B. 10% Answer: (B) 10% Shortcut: the 3rd year's interest = 6,655 − 6,050 = ₹605, earned on ₹6,050. Rate = 605/6050 × 100 = 10% . 1
- Simple interest is charged at 4% per annum for the first 2 years, 6% per annum for the next 3 years and 8% per annum after that. What is the interest on ₹5,000 for 7 years? Answer: C. ₹2100 Answer: (C) ₹2100 Total rate-years = 4 × 2 + 6 × 3 + 8 × 2 = 8 + 18 + 16 = 42%. SI = 42% of 5,000 = ₹2100. 1
- A sum at compound interest amounts to ₹2,420 in 2 years and ₹2,662 in 3 years. What would be the simple interest on the same sum at the same rate for 4 years? Answer: B. ₹800 Answer: (B) ₹800 Rate = 2662 - 2420/2420 × 100 = 10% . Principal = 2420 ÷ 1.21 = ₹2000. SI for 4 years = 2000 × 10 × 4 ÷ 100... 1
- ₹12,000 is lent in two parts, one at 8% and the other at 10% simple interest per annum. The total interest for one year is ₹1,080. How much was lent at 8%? Answer: D. ₹6000 Answer: (D) ₹6000 Shortcut (alligation): average rate = 1080 ÷ 12,000 = 9%. Parts at 8% and 10% are in the ratio (10 − 9) :... 1
- What is the effective annual rate of interest for a nominal rate of 10% per annum compounded half-yearly? Answer: B. 10.25% Answer: (B) 10.25% 5% for two half-years: 5 + 5 + 5 × 5/100 = 10.25%. 1
- The difference between compound interest and simple interest on a sum for 2 years at 5% per annum is ₹15. What is the sum? Answer: C. ₹6000 Answer: (C) ₹6000 CI − SI = P(5/100)² = P/400 = 15, so P = ₹6000. 1
- The simple interest on a sum is one-fourth of the sum, and the rate of interest per annum equals the number of years. What is the rate? Answer: D. 5% Answer: (D) 5% SI = P × R × R/100 = P/4 , so R² = 25 and R = 5%. 1