How much would Greg need to have on deposit at retirement in order to withdraw $35,000 annually over the 15 years if the retirement fund earns 4 percent?
63,000
To find out how much Greg would need to have on deposit at retirement, we can use a formula called the present value of an annuity.
The present value of an annuity formula is:
PV = PMT x [(1 - (1 + r)^-n) / r]
Where:
PV is the present value (the amount Greg needs to have on deposit at retirement).
PMT is the annual withdrawal amount ($35,000).
r is the interest rate per period (4% or 0.04).
n is the number of periods (15 years).
Let's substitute the values into the formula:
PV = $35,000 x [(1 - (1 + 0.04)^-15) / 0.04]
Now, let's calculate it step by step:
1. Calculate (1 + 0.04)^-15:
(1 + 0.04)^-15 ≈ 0.7833
2. Calculate [(1 - 0.7833) / 0.04]:
[(1 - 0.7833) / 0.04] ≈ 4.179
3. Multiply $35,000 by 4.179:
PV ≈ $35,000 x 4.179 ≈ $146,265
Therefore, Greg would need to have approximately $146,265 on deposit at retirement in order to withdraw $35,000 annually over 15 years if the retirement fund earns 4 percent.