The least number of complete years in which a sum of money put out at 20% compound interest will be more than doubled is:
Let’s denote the principal amount as P.
Compound Interest (CI) formula:
CI = P × (1 + R/100)^Time – P
Given values:
R = 20% per annum
We want to find the least number of complete years (Time) for which the amount will be more than doubled, i.e., Amount > 2P.
Amount = P × (1 + 20/100)^Time
= P × (1.2)^Time
We want to find the Time for which:
P × (1.2)^Time > 2P
Divide both sides by P:
(1.2)^Time > 2
Take the logarithm (base 10) of both sides:
Time × log(1.2) > log(2)
Time > log(2) / log(1.2)
Time > 3.802
Since Time must be a whole number (complete years), the least number of complete years is:
Time = 4
The least number of complete years is 4.
