A sum of money triples itself at compound interest in 3 years. What will it…

Under compound interest, the amount after n years is Amount = P(1 + r)n. Over equal-length time blocks, the per-block growth factor multiplies onto itself for each successive block — it does not add.

1. The sum triples in 3 years, so the growth factor for a 3-year block is (1 + r)3 = 3.

2. 9 years is exactly three consecutive 3-year blocks, so the amount after 9 years is P(1 + r)9 = P[(1 + r)3]3.

3. Substituting (1 + r)3 = 3: Amount = P(3)3 = 27P.

Block by block: after the first 3 years the amount is 3P; after the next 3 years it triples again to 3 × 3P = 9P; after the third 3-year block it triples once more to 3 × 9P = 27P — confirming the amount is 27 times the principal after 9 years.