A sum of money becomes three times itself in 3 years at compound interest. What is the rate of interest?

Correct — A. Compound interest multiplies the sum by the same factor, (1 + r⁄100), every year.

Set up: P(1 + r⁄100)³ = 3P
Divide by P: (1 + r⁄100)³ = 3
Take the cube root: 1 + r⁄100 = ∛3 ≈ 1.442
Subtract 1: r⁄100 ≈ 0.442, so r ≈ 44.2% → option (a)

Check: 1.442² ≈ 2.079, and 2.079 × 1.442 ≈ 3.00.

Why the others are wrong

• (b)
  33.3% — 33.3% is too low. At compound interest (4⁄3)³ = 64⁄27 ≈ 2.37, so the sum reaches about 2.37 times itself in 3 years. 33.3% is the simple-interest rate that merely doubles a sum in 3 years.
• (c)
  100% — At 100% the sum doubles every year: 2³ = 8, so it would be 8 times itself after 3 years, not 3 times.
• (d)
  88% — 88% overshoots: 1.88³ ≈ 6.64, so the sum would be more than six times itself after 3 years.

Under compound interest the amount after n years is P(1 + r⁄100)ⁿ. Growth is multiplied, not added, so a target multiple is reached through a root, not a division.

Tripling in 3 years means the yearly factor, cubed, equals 3. The factor is therefore ∛3, and the rate is that factor minus 1.

The same factor answers longer horizons at once: 9 times in 6 years, 27 times in 9 years.

Key facts

• Compound amount: A = P(1 + r⁄100)ⁿ.
• If a sum becomes k times in n years at compound interest, it becomes k² times in 2n years and k³ times in 3n years.
• ∛3 ≈ 1.442, since 1.442³ ≈ 3.00.
• At 100% a year compounded annually, a sum becomes 2ⁿ times itself in n years.

Common traps

• Reading "becomes three times itself" as interest of 3P: the amount is 3P, so the interest earned is 2P.
• Treating it as simple interest: interest of 2P over 3 years gives 66.7% a year, which is not among the options.

No directly related past PYQ was found.