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Answer:
To calculate the single one-time raise needed to cover the rate of inflation over 5 years, we'll use the given information:
- Current income: $69,111
- Projected income after 5 years: $74,757.99
- Inflation rate: 8.17%
Let's break down the steps:
1. **Calculate the inflation factor over 5 years:**
The formula for calculating the future value with inflation is:
\[ \text{Future Value} = \text{Present Value} \times (1 + \text{Inflation Rate})^{\text{Number of Years}} \]
Substituting the values:
\[ \text{Future Value} = 69111 \times (1 + 0.0817)^5 \]
Calculate \( (1 + 0.0817)^5 \):
\[ (1.0817)^5 \approx 1.4692 \]
So,
\[ \text{Future Value} \approx 69111 \times 1.4692 = 101515.61 \]
This is the projected income after accounting for 8.17% annual inflation over 5 years.
2. **Calculate the difference needed as a one-time raise:**
Now, we find the difference between the projected income and the current income:
\[ \text{Difference} = 101515.61 - 69111 = 32404.61 \]
Therefore, the single one-time raise needed after 5 years to cover the rate of inflation is approximately **$32,404.61**.
This amount represents the increase needed to ensure your income keeps up with the projected inflation rate of 8.17% over the next 5 years.