Simple and compound interest
- What equal annual instalment will pay off a debt of ₹3,630 due in 3 years at 10% per annum simple interest? Answer: C. ₹1100 Answer: (C) ₹1100 Instalments paid at the end of years 1, 2 and 3 earn interest for 2, 1 and 0 years until the due date. So... 1
- A loan of ₹2,200 is to be repaid in two equal annual instalments at 20% per annum compound interest. What is each instalment? Answer: D. ₹1440 Answer: (D) ₹1440 The present values of the instalments add up to the loan: x/1.2 + x/1.2² = 2200 . x × 1.2 + 1/1.44 = 2200... 1
- ₹2,210 is divided between A and B so that A's share after 3 years equals B's share after 5 years, both at 10% per annum compound interest. What is A's share? Answer: B. ₹1210 Answer: (B) ₹1210 A(1.1)³ = B(1.1)⁵ , so A/B = (1.1)² = 121/100 . A's share = 121/221 × 2210 = ₹1210 (and B's = ₹1000). 1
- The compound interest on a sum for the 2nd year is ₹1,320 and for the 3rd year is ₹1,452. What is the sum? Answer: A. ₹12,000 Answer: (A) ₹12,000 Rate = 1452 - 1320/1320 × 100 = 10% . 2nd-year interest = P × 1.1 × 0.1 = 0.11P = 1320, so P = ₹12,00... 1
- The simple interest on a sum for 2 years is ₹600 and the compound interest on the same sum at the same rate for 2 years is ₹630. What is the sum? Answer: A. ₹3000 Answer: (A) ₹3000 SI for one year = ₹300. The extra ₹30 in CI is interest on the first year's ₹300, so the rate = 30 ÷ 300... 1
- What is the simple interest on ₹5,000 at 8% per annum for 3 years? Answer: C. ₹1200 Answer: (C) ₹1200 SI = P × R × T/100 = 5000 × 8 × 3/100 = ₹1200. 1
- A sum of money amounts to ₹7,800 in 3 years at 10% per annum simple interest. What is the sum? Answer: A. ₹6000 Answer: (A) ₹6000 In 3 years the sum grows by 30%, so the amount = 1.3 × P. P = 7800 ÷ 1.3 = ₹6000. Trap: taking 30% off ₹7... 1
- At what rate of simple interest will a sum of money double itself in 8 years? Answer: D. 12.5% Answer: (D) 12.5% Doubling means SI = P, i.e. 100% in 8 years. Rate = 100 ÷ 8 = 12.5% per annum. 1
- What is the compound interest on ₹10,000 at 10% per annum for 2 years, compounded annually? Answer: A. ₹2100 Answer: (A) ₹2100 Shortcut: 10% for 2 years = 21% effective (10 + 10 + 1). CI = 21% of 10,000 = ₹2100. Plain: 10,000 × 1.1²... 1
- Find the compound interest on ₹8,000 at 10% per annum for 3 years, compounded annually. Answer: C. ₹2,648 Answer: (C) ₹2,648 Amount = 8000 × (1.1)³ = 8000 × 1.331 = 10648 . CI = 10648 − 8000 = ₹2,648. (₹2,400 is the simple inter... 1
- What is the difference between the compound interest (compounded annually) and the simple interest on ₹10,000 at 10% per annum for 3 years? Answer: C. ₹310 Answer: (C) ₹310 For 3 years, CI − SI = P(R/100)²(3 + R/100) = 10000 × 0.01 × 3.1 = ₹310 . Check: CI = 13310 − 10000 = 3310,... 1