Question

How many monthly withdrawals of $1,400 will an investment of $75,000 sustain if the first withdrawal is made 13 months from now and the money earns 8.4% compounded monthly?

Answer 1

Solution

First, we need to calculate the future value of 75000 at the end of 12 months

FV(Future value) = Amount*(1+r)^n

Since this is a monthly compounding

Therefore

FV(Future value) = Amount*(1+r/12)^n*12

n= number of years= 1 year in this case

r= Annual interest= 8.4% in this case

Future value=75000(1+.084/12)^12

=81548.300

Now this will become the opening principal at the starting of 13th month from which withdrawal will be made( 1400 per month) and the balance amount will keep earning the interest of 8.4% per annum

The calculations are given below

Excel formula used

Therefore as it can be seen from the calculations the amount left in the account after the withdrawal of 87th month( from the first month of deposit of 75000) is around 128, therefore, this is the last month after which no withdrawal of 1400 is possible

So the total withdrawals that can be sustained = 13 months to 87th month

=75 months