Present Value - Future Value Amortization Schedule
This topic is covered in detail by an excellent article, Reverse mortgages fraught with pitfalls by Business Editor, Ellen Roseman, Toronto Star, July 20th 2003. The mathematical aspects, that will be covered here are actually quite simple because a reverse mortgage is just another name for a negative amortization schedule.
Assume your home has a current market value of $400,000. A reverse mortgage company would give you say 30% of that value in cash. You now have $120,000 in your hand and have a loan for the next ten years where you do not make any payments (a negative amortization schedule) and the monthly interest accrues and is compounded semi-annually. The reverse mortgage company actually adjusts the annual interest rate every year but for the sake of the example we will choose a constant 7.25% which is the going rate in Canada in 2003.
You simply generate an amortization schedule for 10 years at 7.25% for monthly payments on a principal of $120,000 and then do a negative amortization schedule by making all the payments zero. If one wanted to verify the reverse mortgage companies calculations it would be a simple matter of inserting the appropriate interest rate for each year before doing the negative amortization schedule.
After 10 ten years you would owe the reverse mortgage company $244,608.81