A sum of money tripled itself at compound interest in 10 years. In how many…

Concept

Under compound interest a principal grows geometrically: after t years the amount is P(1+r)t, so the growth factor (1+r)t is multiplicative. A fixed length of time always multiplies the money by the same factor, regardless of when it starts, so each repetition of that interval multiplies the existing amount by that factor again.

Application

1. Tripling in 10 years means (1+r)10 = 3, so one 10-year block multiplies the money by 3.

2. The target is 27 times the original, and 27 = 3 x 3 x 3 = 33.

3. Each factor of 3 is produced by one 10-year block, so reaching 33 needs that block to repeat 3 times.

4. Total time = 3 x 10 = 30 years.

Cross-check

(1+r)30 = ((1+r)10)3 = 33 = 27, which is exactly 27 times the principal, confirming 30 years.