A builder is offering $$115,777$ loans for his properties at $9$ percent for $25$ years. Monthly payments are based on current market rates of $9\mathrm{.}5$ percent and are to be fully amortized over $25$ years. The property would normally sell for $$130,000$ without any special financing.

Required:

a$.$ At what price should the builder sell the properties to earn, in effect, the market rate of interest on the loan? Assume that the buyer would have the loan for the entire term of $25$ years.

b$.$ At what price should the builder sell the properties to earn, in effect, the market rate of interest on the loan if the property is resold after $10$ years and the loan repaid?