A sum doubles in 5 years at simple interest. What is the annual rate?

Correct — D.
Rule: simple interest = P × R × T ⁄ 100.

Doubling means the interest equals the sum itself:
SI = P

P = P × R × 5 ⁄ 100
1 = 5R ⁄ 100
R = 100 ⁄ 5 = 20% → option (d).

Why the others are wrong

• (a)
  10% — At 10% five years earn 10 × 5 = 50% of the sum, so the amount reaches 1.5 times, not 2. Doubling at 10% takes 10 years.
• (b)
  12% — At 12% five years earn 60% of the sum, an amount of 1.6 times. Doubling at 12% would take 100 ⁄ 12 = 8⅓ years.
• (c)
  15% — At 15% five years earn 75% of the sum, an amount of 1.75 times. Doubling at 15% takes 100 ⁄ 15 = 6⅔ years.

Under simple interest the interest is worked out on the original sum every year, so it grows in equal steps. A sum doubles when the total interest equals the principal, which happens when R × T = 100.

That gives a shortcut worth carrying: the rate for doubling is 100 ⁄ T, and the time is 100 ⁄ R. Here T = 5, so R = 20%.

Key facts

• Simple interest = P × R × T ⁄ 100.
• A sum doubles under simple interest when R × T = 100.
• A sum becomes n times under simple interest when R × T = 100 × (n − 1).

Common traps

• Treating 'doubles' as interest of 2P. The amount is 2P, so the interest is P.
• Carrying compound-interest habits over: at simple interest a sum that doubles in 5 years is 3 times, not 4 times, after 10.

No directly related past PYQ was found.