A sum of money placed at compound interest triples itself in 8 years. In how many years will it amount to 243 times itself?Options15 years27 years80 years40 years
Question
A sum of money placed at compound interest triples itself in 8 years. In how many years will it amount to 243 times itself?Options15 years27 years80 years40 years
Solution
The problem involves compound interest and the concept of tripling the initial amount.
Given that the sum of money triples itself in 8 years, this means that the money increases by a factor of 3 every 8 years.
We need to find out how many years it will take for the money to increase by a factor of 243.
Since 243 is 3^5, this means that the money needs to triple itself 5 times.
Since it takes 8 years for the money to triple itself once, it will take 5 * 8 = 40 years for the money to triple itself 5 times.
Therefore, the money will amount to 243 times itself in 40 years.
So, the correct option is 40 years.
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