In: Finance
You are planning to make a total of 30 annual withdrawals of $350,000 after retirement. After retirement you will be able to earn 5 percent per year
Therefore Present value of the total of 30 annual withdrawals of $350,000 at the time of retirement can be calculated with the help of PV of an Annuity formula
PV1 = PMT * [1-(1+i) ^-n)]/i
Where,
Present value at the time of retirement (PV) =?
PMT = Annual payment = $350,000
n = N = number of payments = 30 years
i = I/Y = interest rate per year =5%
Therefore,
PV1 = $350,000* [1- (1+5%) ^-30]/5%
= $5,380,357.86
In addition, you’d like to have an additional $85,000 in your fifth year of retirement to buy a boat
Therefore PV of this amount at the time of retirement
PV2 = FV/ (1+i) ^n
Where,
Present Value PV =?
Future value FV=$85,000
Annual interest rate i = 5%
Time period n = 5 years
Therefore,
PV2 = $85,000/ (1+5%) ^5
= $66,599.72
Total amount required at the time of retirement = PV1 + PV2 = $5,380,357.86 + $66,599.72
= $5,446,957.58 (Now this amount will be future value of all savings)
Your retirement account will have $5,446,957.58
We can use FV of an Annuity formula to calculate the annual savings by you
FV = PMT *{(1+i) ^n−1} / i
Where,
Future value of annual savings FV = $5,446,957.58
PMT = Annual savings =?
n = N = number of payments = 35 years
i = I/Y = interest rate per year =8%
Therefore,
$5,446,957.58 = Annual savings *{(1+8%) ^35−1} /8%
Annual savings = $31,610.14
Therefore you have to save $31,610.14 per year to achieve your retirement goal.