Based on the given information, you believe you will spend $100,000 a year for 15 years once you retire in 10 years. The interest rate is 12.50% per year.
To calculate the amount of money you will need at retirement, we can use the formula for the future value of an annuity:
\[FV = P \times \left( \frac{{(1 + r)^n - 1}}{r} \right)\]
Where:
- FV is the future value of the annuity
- P is the annual payment or expenditure
- r is the interest rate per period (in this case, per year)
- n is the number of periods (in this case, the number of years)
Plugging in the values:
- P = $100,000
- r = 12.50% or 0.125
- n = 15
\[FV = 100,000 \times \left( \frac{{(1 + 0.125)^{15} - 1}}{0.125} \right)\]
Calculating this expression, we find that the future value of the annuity is approximately $2,767,512.68.
Therefore, the main answer is that you will need approximately $2,767,512.68 at retirement to cover your annual expenditure of $100,000 for 15 years.
In conclusion, by using the formula for the future value of an annuity, we can determine the amount of money you will need at retirement based on your expected annual expenditure and the interest rate.