Answer :
To determine what you will need to earn at age 65 to maintain your standard of living, given that inflation stays at 6% per year, we can use the concept of compound interest. Here is a detailed, step-by-step solution:
### Step-by-Step Solution:
1. Identify the Information Provided:
- Current Age: 30 years old (assuming as it is not explicitly given)
- Current Salary: [tex]$50,000 (assuming as it is not explicitly given) - Inflation Rate: 6% per year - Target Age: 65 years old 2. Calculate the Number of Years Until Retirement: \[ \text{Years until 65} = \text{Target Age} - \text{Current Age} = 65 - 30 = 35 \text{ years} \] 3. Understand the Compound Interest Formula: To find the future salary needed, we use the formula for compound interest: \[ \text{Future Value} = \text{Present Value} \times (1 + \text{Rate})^\text{Number of Periods} \] In this context: - Present Value (PV): Current Salary = $[/tex]50,000
- Rate: Inflation rate = 0.06 (6%)
- Number of Periods (n): Years until retirement = 35
4. Calculate the Future Salary:
Substitute the values into the formula:
[tex]\[ \text{Future Salary} = 50000 \times (1 + 0.06)^{35} \][/tex]
To simplify the calculations:
[tex]\[ 1 + \text{Rate} = 1 + 0.06 = 1.06 \][/tex]
Therefore:
[tex]\[ \text{Future Salary} = 50000 \times (1.06)^{35} \][/tex]
5. Calculate [tex]\( (1.06)^{35} \)[/tex]:
Using a calculator:
[tex]\[ (1.06)^{35} \approx 7.6861 \][/tex]
6. Calculate the Future Salary:
[tex]\[ \text{Future Salary} = 50000 \times 7.6861 = 384305 \][/tex]
### Conclusion:
To maintain your current standard of living, you will need to earn approximately $384,305 per year at age 65, assuming inflation remains constant at 6% per year.
### Step-by-Step Solution:
1. Identify the Information Provided:
- Current Age: 30 years old (assuming as it is not explicitly given)
- Current Salary: [tex]$50,000 (assuming as it is not explicitly given) - Inflation Rate: 6% per year - Target Age: 65 years old 2. Calculate the Number of Years Until Retirement: \[ \text{Years until 65} = \text{Target Age} - \text{Current Age} = 65 - 30 = 35 \text{ years} \] 3. Understand the Compound Interest Formula: To find the future salary needed, we use the formula for compound interest: \[ \text{Future Value} = \text{Present Value} \times (1 + \text{Rate})^\text{Number of Periods} \] In this context: - Present Value (PV): Current Salary = $[/tex]50,000
- Rate: Inflation rate = 0.06 (6%)
- Number of Periods (n): Years until retirement = 35
4. Calculate the Future Salary:
Substitute the values into the formula:
[tex]\[ \text{Future Salary} = 50000 \times (1 + 0.06)^{35} \][/tex]
To simplify the calculations:
[tex]\[ 1 + \text{Rate} = 1 + 0.06 = 1.06 \][/tex]
Therefore:
[tex]\[ \text{Future Salary} = 50000 \times (1.06)^{35} \][/tex]
5. Calculate [tex]\( (1.06)^{35} \)[/tex]:
Using a calculator:
[tex]\[ (1.06)^{35} \approx 7.6861 \][/tex]
6. Calculate the Future Salary:
[tex]\[ \text{Future Salary} = 50000 \times 7.6861 = 384305 \][/tex]
### Conclusion:
To maintain your current standard of living, you will need to earn approximately $384,305 per year at age 65, assuming inflation remains constant at 6% per year.
