Serge M. answered 12/21/16
Professor of Accounting, retired. Ph.D., CPA
You have the future value of an annuity and you have to find the monthly rent. This can be done by solving a formula, using a spreadsheet function, or a calculator. The calculator is simplest, but you have to understand compound interest and annuity concepts. They are important and you will face them all your life, so it is worth learning this material.
You are dealing with five variables, and you can solve for any one of them if you know the other four. In this problem the variables are:
PV = present value of an ordinary annuity = 0
FV = future value of an ordinary annuity = $600,000
N = number of periods over which compounding takes place = 40 years x 12 months - 480 months
i% - the compounding interest rate = 4.8% / 12 = .4% per month
PMT = the periodic payment (rent) of an ordinary annuity = ?. This is what we want to find.
The solution is $412.51
This amount invested every month for 40 years will grow to $600,000
How much interest will you earn? Simple! $600,000 less the amount you invested which is 412.51 x 480. I'll let you solve this.
To achieve your goal in 20 years, we only need to change N to 240 and solve for the new PMT. We get $1,4876.79
Now that we have PMT for 20 years we can change N to 120 and solve for FV. $229,486.94