How much of the initial investment's value could be lost after 15 years at 3% inflation?

To determine how much of the initial investment's value could be lost after 15 years at an inflation rate of 3%, we can use the concept of the purchasing power of money. Inflation erodes the real value of money over time, meaning that the money you have today will buy less in the future if inflation remains positive.

The formula to compute the real value of an investment after a certain number of years considering inflation is:

[

\text{Real Value} = \text{Initial Investment} \times \left( \frac{1}{(1 + \text{inflation rate})^{n}} \right)

]

where ( n ) is the number of years.

In this scenario, with an inflation rate of 3% over 15 years, we calculate it as follows:

[

\text{Real Value} = 1 \times \left( \frac{1}{(1 + 0.03)^{15}} \right)

]

Calculating this:

• ( (1.03)^{15} \approx 1.557 )

Using this, the real value of the initial investment becomes:

[

\text{Real Value} \approx \frac{1}{1