A sum of money place at compound interest doubles itself in 4 years. In how…

Key idea: if a sum doubles in 4 years, each 4-year period multiplies the amount by 2.

• Using repeated doubling: To get eight times the original amount we need a factor of 8 = 2^3, i.e. three doublings. Each doubling takes 4 years, so time = 3 × 4 = 12 years.

• Algebraic check using compound interest: Let (1 + r) be the growth factor per year. Doubling in 4 years gives (1 + r)^4 = 2, so (1 + r) = 2^(1/4).

• We want (1 + r)^t = 8. Substitute (1 + r) = 2^(1/4): (2^(1/4))^t = 8, so 2^(t/4) = 2^3, which gives t/4 = 3 and hence t = 12.

Therefore the sum will amount to eight times itself in 12 years.