If you buy a factory for $250,000 and the terms are 20% down, the
balance to be paid off over 30 years at a 12% rate of interest on the
unpaid balance, what are the 30 equal annual payments?

jax26-ga:

The formula you need to apply here, is that for an annuity given present value:

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

where A = annual payment
      PV= present value of debt
      r = annual interest rate on debt
      n = number of periods for payment

You stated that the factory is purchased for a value of $250,000 with
20% down (ie. $50,000 on Day 0), and the balance to be paid off over
30 years at a 12%/yr interest rate. Since you specify that there are
30 equal annual payments over 30 years, we can approach this as
payments occurring at the end of each period, hence the above formula.
With the down-payment deducted from the problem since it occurs on Day
0, the PV is therefore $200,000, r is 12%, and n is 30 (years).
Running these through the formula gives you:

     A = $200,000 * [ 0.12 / [ 1 - [ 1 / 1.12^30 ] ] ]
  
     A = $200,000 * [ 0.12 / 0.966 ]

     A = $200,000 * 0.124

     A = $24828.73

You can see this for yourself using Excel; start with $200,000 in
Column A. In column B, you have "=A1*1.12-24828.73" (in other words,
calculate a year's worth of interest on the principal, then deduct the
payment). Drag that formula across 30 columns (to column AE), and
you'll have a balance of zero after the 30th annual payment is made.

I hope this helps!

aht-ga
Google Answers Researcher

Thank you for your time.