Question

A buyer can afford no more than $500 per month for mortgage payments (principal and interest). The most favorable loan availabe to him requires monthly payments for 30 years at 10%. If the lender allows a maximum loan to value ration of 90%, what is the most expensive house the borrower can purchase assuming he has the necessary down payment?

Answer 1

PV of annuity for making pthly payment
P = PMT x (((1-(1 + r) ^- n)) / i)
Where:
P = the present value of an annuity stream
PMT = the dollar amount of each annuity payment
r = the effective interest rate (also known as the discount rate)
i=nominal Interest rate
n = the number of periods in which payments will be made
Nominal rate	10%
Effective rate	=((1+10%/12)^12)-1)
Effective rate	10.47%
monthly payment	500
Annual payment	6000
PV of payment	= 6000 * (((1-(1 + 10.47%) ^- 30)) / 10%)
PV of payment	56,974
Loan to value ratio	90%
Maximum value of house	=56974/90%
Maximum value of house	63,304
so maximum cost, he can afford with this loan is 63,304