In approximately 13 years, the money will be five times its original value.
To solve this problem, we can use the concept of compound interest. When a certain sum of money trebles itself, it means it increases by three times its original value.
In the given scenario, the money trebles itself in 8 years. This means that the sum of money increases by a factor of 3 in 8 years.
Now, we need to find out how many years it will take for the money to be five times its original value.
Let's break down the problem step by step:
1. We know that the money trebles itself in 8 years. So, in 8 years, the money increases by a factor of 3.
2. To find the time it takes for the money to be five times its original value, we can set up a proportion:
3/8 = 5/x
Here, x represents the number of years it takes for the money to be five times its original value.
3. Cross-multiplying the proportion gives us:
3x = 8 * 5
4. Solving for x, we get:
3x = 40
x = 40/3
x ≈ 13.33
Therefore, it will take approximately 13.33 years for the money to be five times its original value.
Since time cannot be measured in fractions of a year, we need to round the answer to the nearest whole number. In this case, the closest whole number is 13.
So, in approximately 13 years, the money will be five times its original value.