Omar's current annual salary is $75,000. How much will he need to earn 15 years from now to retain his present purchasing power if the rate of inflation over that period is 2%/year? Assume that inflation is continuously compounded.
To calculate the future salary amount required to retain Omar's present purchasing power, we need to take into account the effect of inflation over time. Since inflation is continuously compounded, we can use the formula for compound interest:
Future Value = Present Value * e^(rate * time)
Where:
- Future Value is the amount Omar needs to earn 15 years from now
- Present Value is Omar's current salary ($75,000)
- rate is the rate of inflation (2% or 0.02 in decimal form)
- time is the number of years (15)
Let's calculate it step by step.
1. Convert the rate of inflation into decimal form: 2% = 0.02.
2. Substitute the values into the formula:
Future Value = $75,000 * e^(0.02 * 15)
3. Calculate the exponential part:
Future Value = $75,000 * e^(0.3)
4. Determine the value of 'e'. 'e' is a mathematical constant approximately equal to 2.71828.
Future Value = $75,000 * 2.71828^(0.3)
5. Calculate the exponential part:
Future Value = $75,000 * 1.3498588
6. Multiply the present salary by the exponential part to find the future value:
Future Value = $101,239.41
Therefore, to retain his present purchasing power, Omar will need to earn approximately $101,239.41 15 years from now, considering a 2% annual inflation rate (compounded continuously).