What principal would amount to ₹21,420 in 2 years at the rate of 9.5% p.a. simple interest?

Correct — D. Two years at 9.5% simple interest is 19% of the principal, so the amount is 1.19 times the principal.

1.19 × P = ₹21,420
P = 21,420 ⁄ 1.19 = ₹18,000

Check it forward: 9.5% of 18,000 = ₹1,710 a year, so ₹3,420 over two years, and 18,000 + 3,420 = ₹21,420 → option (d)

Why the others are wrong

• (a)
  ₹16,000 — ₹16,000 grows to 1.19 × 16,000 = ₹19,040 in two years, ₹2,380 short of ₹21,420. The gap is too wide to be a rounding difference.
• (b)
  ₹12,000 — ₹12,000 reaches only ₹14,280 at 9.5% for two years. To arrive at ₹21,420 from ₹12,000 you would need a rate near 39% a year.
• (c)
  ₹11,273 — ₹11,273 is 21,420 ⁄ 1.9 — a decimal slip that treats two years of 9.5% as 90% of the principal instead of 19%.

Simple interest is charged on the original principal every year and never on interest already earned.

So over t years at r% the interest is P × r × t ⁄ 100 and the amount is P(1 + rt ⁄ 100). Here rt ⁄ 100 = 19 ⁄ 100, giving the multiplier 1.19.

Working through the multiplier turns an amount question into a single division. Writing it out long, as 21,420 = x + 19x ⁄ 100, lands in the same place but costs you a line.

Key facts

• Amount under simple interest = P(1 + rt ⁄ 100), so 9.5% for 2 years gives the multiplier 1.19.
• The interest here is ₹3,420, made of ₹1,710 in each of the two years.
• Simple interest is equal in every year, which is what lets you add the rates before dividing.
• The same ₹18,000 compounded yearly at 9.5% would amount to ₹21,582.45, because the second year earns on ₹19,710.

Common traps

• Dividing ₹21,420 by 1.095 or by 1.9 instead of by the correct 1.19.
• Subtracting 19% from ₹21,420, which gives ₹17,350.20 and is not the principal.
• Reading ₹21,420 as the interest earned rather than as the amount.

No directly related past PYQ was found.