your are planning to retire in twenty years. you want to be able to draw your savings at the rate of $10,000 per end of year. How much would you have to pay in equal annual deposits until retirement to meet your objectives. assume interest remain at 9%
Answer
To calculate the equal annual deposits required to meet your retirement goal, we will use the concept of annuity. An annuity is a series of equal payments made at regular intervals. In this case, deposits made annually.
Here is the step-by-step calculation:
1. Determine the future value (FV) you want to accumulate. In this case, you want to be able to draw $10,000 per year for 20 years. Therefore, the future value is:
FV = $10,000 * 20 = $200,000
2. Determine the interest rate per period. Since the interest remains at 9% and the deposits are made annually, the interest rate per period is also 9%.
3. Use the future value of an ordinary annuity formula to calculate the equal annual deposits (PMT). The formula is:
PMT = FV * (i / ((1 + i)^n - 1))
Where:
- PMT = equal annual deposits
- FV = future value
- i = interest rate per period
- n = number of periods
Let's substitute the values into the formula:
PMT = $200,000 * (0.09 / ((1 + 0.09)^20 - 1))
Calculating this, we find:
PMT ≈ $4,720.65
Therefore, you would need to make equal annual deposits of approximately $4,720.65 until retirement to meet your objective of being able to draw $10,000 per year for 20 years, assuming the interest rate remains at 9%.