Tony Quincy wants to withdraw 33300 each year for 11 years f

Tony Quincy wants to withdraw $33,300 each year for 11 years from a fund that earns 6% interest.

How much must he invest today if the first withdrawal is at year-end? How much must he invest today if the first withdrawal takes place immediately? (Round factor values to 5 decimal places, e.g. 1.25124 and final answers to 0 decimal places, e.g. 458,581.)

First withdrawal at year-end $

First withdrawal immediately $

Solution

First withdrawal at year-end :

Investment amount = P

formula = Installment = P * i * (1 + i)^n / (1 + i)^n - 1

=> 33300 = P * 0.06 * (1 + 0.06)^11 / (1 + 0.06)^11 - 1

=> 33300 = P * 0.06 * 1.898298 / 1.898298 - 1

=> P = 262632.84

First withdrawal immediately: if first installment withdrawan immediately, then future tenure reduced to 10 years

=> 33300 = [P * 0.06 * (1 + 0.06)^10 / (1 + 0.06)^10 - 1] + 33300

=> 33300 = [P * 0.06 * 1.790848 / 1.790848 - 1] + 33300

=> P = 245090.95 + 33300 = 278390.95