Numerical answer
A sum of money triples itself in 8 years at a certain rate of simple interest. In how many years will it become 7 times itself, at the same rate of interest?
Show answer and solution
Answer: 24
If the sum is P, tripling means the interest earned equals 2P in 8 years. So the rate gives 2P = P·r·8 → r = 1/4 (i.e. 25% p.a.).
To become 7 times itself, the interest needed is 6P. Time T satisfies 6P = P·r·T = P·(1/4)·T → T = 24.
Answer: 24 years.
Shortcut: interest earned is proportional to time, so time scales with the multiple-minus-one: (7−1)/(3−1) × 8 = 3 × 8 = 24.
To become 7 times itself, the interest needed is 6P. Time T satisfies 6P = P·r·T = P·(1/4)·T → T = 24.
Answer: 24 years.
Shortcut: interest earned is proportional to time, so time scales with the multiple-minus-one: (7−1)/(3−1) × 8 = 3 × 8 = 24.
Saved on this device. Sign in or create a free account to keep it on every device.