Question

please choose one answer

Kate is now 40 years old, plans to retire in 25 years, and expects to live for 20 years after she retires. She wants a fixed retirement income of $90,000 per year. Her retirement income will start from the day she retires. Kate expects to earn a return of 8% per year. How much must she save at the end of each of the next 25 years to meet her retirement goal? A. $883,629 OB. $12,087 C. $13,054 O D. $954,319

Answer 1

Suppose that amount be $ X

At the end of first year, value of the savings = $X(1.08)

At the end of second year, value of the savings= $X(1.08)+ $X(1.08)^2

At the end of third year, value of the savings= $X(1.08)+ $X(1.08)^2+ $X(1.08)^3

At the end of the 24th year (or in the starting of 25th year) value of the saving will be:

X(1.08+1.08^2+1.08^3+..........................................+1.08^24) (Assume it as equation 1)

Now when Kate will be 65, she must be having $90000 per year for the next 20 years.

We know that

present value of annuity= P (1-(1+R)^-N)/R

Here P is $90000

Therefore, Present value of Annuity= 90000(1-(1.08)^-20)/.08

After solving it, we find that Present value of annuity at the time of kate being 65 will be $883629

Now equation 1 should be equal to $883629

X(1.08+1.08^2+1.08^3+1.08^4+..................1.08^24)= 883629

solving for X we will get our solution as $ 12087