Question

Anna has just completed her undergraduate degree and is already planning to enter an MBA program one year from today. The MBA tuition will be $7,000 per year for 2 years, paid at the beginning of each year. In addition, Anna would like to retire 20 years from today and spend $50,000 every year for 10 years (years 20-29, withdrawn at the beginning of each year). To fund her expenditures, Anna will save money at the end of year 0 and at the end of years 3-19. At the end of year 29, she wants to have nothing in her bank account. Do not enter a comma or dollar sign.

Assuming that the interest rate is 5%, calculate the constant annual dollar amount that she must save at the end of each of these years to cover all of her expenditures (tuition and retirement).

If the retirement spending increases to $60,000, what is the constant annual dollar amount that she must save?

Answer 1

Annual tuition fee = C_t = 7,000 at the end of t = 1 and t = 2

Post retirement annual expenses = C_r = 50,000 at the end of t= 20 through t= 29

Discount rate, R = 5%

PV of all the cash flows required, at t = 0

=PV (0.05, 2, -7000) + PV (0.05, 29, -50000) - PV (0.05, 19, -50000) =  13,015.87 + 757,053.68 - 604,266.04 = 165,803.51

Let the constant annual dollar amount that she must save at the end of each of these years (t = 0, and from t = 3 through t = 19) to cover all of her expenditures (tuition and retirement) = A

Then, PV of all the inflows

= C + C x [PV (0.05,19,1) - PV (0.05,2,1)]

= C + C x [ 12.085320860 -  1.859410431] = C x 11.22591043

Hence, we get the equation as:

165,803.51 = C x 11.22591043

Hence, C = 165,803.51 / 11.22591043 =  14,769.7161

Hence, the constant dollar amount to save = C = $ 14,770

(rounded off to the nearest decimal, you can round it off as per your requirement)