Simon wishes to have $400,000 in a retirement fund 20 years from now. He can create the retirement fund by making a single lump sum deposit today.
How much would Simon need to have on deposit at retirement in order to withdraw $35,000 annually over the 15 years if the retirement funds earns 8
%?
You have conflicting information.
At the beginning of his "retirement period" he will need:
35000( 1 - 1.08^-15)/.08
= 299,581.75
so he would not need $400,000 at that time.
To assure that he will have that $299,581.75 available 20 years from now , he needs a present deposit of
299581.75(1.08)^-20
or
$ 64,274.73
If he wanted $400,000 twenty years from now he would have to make a deposit now of
400,000(1.08)^-20
or $85,819.28
This would supply him with quite a bit more to withdraw annual payments.
Let that payment be P
solve:
400,000 = P( 1 - 1.08^-15)/.08
P = $ 46,731.82
To calculate how much Simon would need to have on deposit at retirement, we can use the future value of an annuity formula. Here's how you can calculate it step by step:
Step 1: Calculate the future value of the annuity.
The future value of an annuity formula is given by:
FV = P * (1 + r)^n - 1 / r
Where:
FV = Future value of the annuity
P = Annual withdrawal amount
r = Annual interest rate
n = Number of years
Using the given information:
P = $35,000 (annual withdrawal amount)
r = 8% (annual interest rate)
n = 15 years (number of years)
FV = $35,000 * (1 + 0.08)^15 - 1 / 0.08
Step 2: Calculate the lump sum deposit needed today.
To calculate the lump sum deposit needed today, we need to find the present value of the annuity. The present value of an annuity formula is the reverse of the future value formula:
PV = FV / (1 + r)^n
Using the calculated future value (FV) from step 1:
PV = FV / (1 + 0.08)^15
Step 3: Calculate the lump sum deposit needed today.
Now, we calculate the lump sum deposit needed today by subtracting the present value (PV) from the future value (FV).
Deposit = FV - PV
Substituting the calculated values and solving the equation will give us the deposit needed:
Deposit = $35,000 * (1 + 0.08)^15 - 1 / 0.08 - FV / (1 + 0.08)^15
By plugging in the values into the formula, you can calculate the deposit needed for Simon to have $400,000 in retirement and withdraw $35,000 annually over 15 years with an 8% interest rate.