Question

Sofia just graduated from college and she is starting her new job today. Her new employer gave her a $15,000 signing bonus that she will invest today. She plans to retire 50 years from today (i.e., at the end of year 50). Once she retires, she would like to be able to withdraw from her retirement account $180,000 at the end of each year, starting the year after she retires (i.e., year 51). She expects that her retirement will last for 20 years (and the amount in her account after that should be 0). If Sofia can earn a return of 9% on her investments for the first 50 years and then 4% once she retires, how much money (in equal payments) does she need to save and invest each year in the first 50 years of her life to meet her goal (she invests ar the end of the year, i.e. this an ordinary annuity)? Round to the nearest 2 decimal places - if for example the answer is 7,345.567 then round it to 7,345.57.

Answer 1

Sofia would lile to withdraw $180,000 at the end of each year of her retirement for 20 years = $180,000

Calculating the Present Value of periodic withdrawals at year 50 from today using ordinary annuity formula:-

Where, C= Periodic Payments = $180,000

r = Periodic Interest rate = 4%

n= no of periods = 20 years

Present Value = $2,446,258.74

So, the amount Sofia need at retiremnet is $2,446,258.74

Now, As Sofia received as Bonus of $15,000 which she invested in her retirement account. Along with the Initial deposit Sofia would like to contribute periodic deposit into retirement account such that future value of both Periodic as well as initial depoosit will be $2,446,258.74

Calculating the Periodic Deposit of Sofia:-

Where, C= Periodic Deposits

r = Periodic Interest rate = 9%

n= no of periods = 50

Initial Depsoit = $15,000

C = $1632.83

So, the money (in equal payments) does she need to save and invest each year in the first 50 years of her life to meet her goal is 1632.83