Simple & Compound Interest MCQs for UPSC Prelims

Same principal P grows to the same amount Q in one year under both schemes, so P(1 + R/200)^2 = P(1 + S/100). Expanding: 1 + R/100 + R^2/40000 = 1 + S/100, hence S = R + R^2/400. Since R > 0, S exceeds R, i.e. R < S - option (c). Intuitively, half-yearly compounding earns interest on interest within the year, so a smaller nominal rate R suffices to match the annually compounded rate S. Option (a) ignores intra-year compounding, option (b) reverses the inequality, and option (d) wrongly allows equality, which would need R = 0.

Interest rate 12.5% = 1/8, so each year the balance is multiplied by 1.125. Year 1: 22,800 x 1.125 = 25,650; after paying 8,650, balance = 17,000. Year 2: 17,000 x 1.125 = 19,125; after paying 9,125, balance = 10,000. Year 3: 10,000 x 1.125 = 11,250, which must be paid in full to clear the debt. Answer is Rs. 11,250.

$\frac{7290}{6250} = 1.1664 = 1.08^2$, so the rate is 8%. The value 16.64% is the total growth over two years, 8.32% halves that as if it were simple interest, and 11.66% misreads the growth factor 1.1664 as a percentage.

Interest per year = 8% of 2,500 = 200, so 1,000 needs $\frac{1000}{200} = 5$ years. The value 12.5 is the time for the deposit to double, 20 comes from inverting the formula ($\frac{2500 \times 8}{1000}$), and 8 simply repeats the rate.

Simple interest is the same every year: 6% of 5,000 = 300 in the fourth year, just as in the first. The value 1,200 is the interest for all four years, 357.30 is the fourth-year interest under annual compounding, and 5,300 is the amount after one year.

Second-year interest = 1,664 - 800 = 864, which is 8% more than 800, so the rate is 8%. Then the sum = $\frac{800}{0.08} = 10000$. The value 20,800 divides the two-year total by the rate, 10,400 uses the average interest of 832 per year, and 10,800 is the balance after the first year, not the original sum.

After 2 years: $10000 \times 1.1^2 = 12100$. The last half-year adds 5% of that: 12,100 × 1.05 = 12,705. The value 12,500 is simple interest throughout, 12,600 adds the half-year interest on the original 10,000 only, and 12,100 stops after 2 years.

Simple interest for 3 years = 8000 x 10 x 3 / 100 = Rs. 2,400. Compound amount = 8000 x (1.1)^3 = 8000 x 1.331 = Rs. 10,648, so CI = 2,648. Difference = 2,648 - 2,400 = Rs. 248. This matches the formula for the 3-year difference: P(r/100)^2 x (3 + r/100) = 8000 x 0.01 x 3.1 = 248.