Question

# Sofia just graduated from college and she is starting her new job today. Her new employer...

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.

1.
Calculation of amount required at the time of retirement:

PMT = \$180,000
Nper = 20
Rate = 4%
FV = 0

Amount required at the time of retirement can be calculated by using the following excel formula:
=PV(rate,nper,pmt,fv)
=PV(4%,20,-180000,0)
= \$2,446,258.74

Calculation of annual deposit:

FV = \$2,446,258.74
Rate = 9%
Nper = 50
PV = \$15,000

Annual deposit can be calculated by using the following excel formula:
=PMT(rate,nper,pv,fv)
=PMT(9%,50,15000,-2446258.74)
= \$1,632.83

Annual deposit = \$1,632.83

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