Question

Clarissa just graduated from High school 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

First we need to calculate present value at the start of her retirement i.e. 51st year of $180,000 withdrawal at 4%.

we can use financial calculator for calculation of present value at the start of her retirement with below keystrokes.

N = no. of retirement years = 20; I/Y = interest rate = 4%; PMT = annual withdrawal = -$180,000; FV = future value = $0 > CPT = compute > PV = present value = $2,446,258.74

PMT needs to be entered as negative value as it's a cash outflow.

so, she needs to have $2,446,258.74 at the start of retirement to able to withdraw $180,000 for 20 years.

now using $2,446,258.74 as future value we can calculate annual saving and investment amount for 50 years.

N = no. of years = 50; I/Y = interest rate = 9%; PV = present value = -$15,000; FV = future value = $2,446,258.74 > CPT = compute > PMT = annual saving and investment amount = $1,632.83

PV needs to be entered as negative value because it's a cash outflow.

she needs to save and invest $1,632.83 each year in the first 50 years of her life to meet her goal.