Question

Georgia wants to build a retirement portfolio. If she invests at 7% per year, she'll be able to generate a $3000 monthly income for 30 years. She still has 20 years until she retires and hasn't started saving yet. What does she need to contribute each month to reach her goal?

Answer 1

First of all lets calculate amount of money that will be required at end of 20 years

here she needs monthly 3000$ hence A = 3000$ , rate of interest = 7%/12 = , n = no of months = 30*12 = 360

PV(Annuity) = A[1-(1/(1+r)^n / r]

=3000[1-(1/(1+0.5833%)^360 / 0.005833]

=3000[1-(1/1.005833)^360 / 0.005833]

=3000[1-(0.1232) / 0.005833]

=3000[0.8768/0.005833]

=3000[150.3136]

=450940.912$

Now let us calculate amount that she has to deposit every month to get $450940.912

FV(annuity) =A [(1+r)^n - 1 / r]

Here n = 20*12 = 240

450940.912 = A[(1+0.005833)^240 - 1 /0.005833]

=450940.912 = A[4.038417 - 1 /0.005833]

450940.912 = A(520.9014)

A = 865.69 $

Thus she need to keep every month 865.69$ for 20 years