Problem $1$Suppose a homeowner has an existing mortgage loan with these terms: Remaining balance of $$150,000,$ interest rate of $8$ percent, and remaining term of $10$ years $($monthly payments$).$ This loan can be replaced by a loan at an interest rate of $6$ percent, at a cost of $8$ percent of the outstanding loan amount.a$.$ What is the net benefit of refinancing?b$.$ What is the NPV if the homeowner expects to be in the home for only five more years?Problem $2$Assume an elderly couple owns a $$140,000$ home that is free and clear of mortgage debt. A reverse annuity mortgage $($RAM$)$ lender has agreed to a $$100,000$ RAM. The loan term is $12$ years, the contract interest rate is $9\mathrm{.}25$ percent, and payments will be made at the end of each month.a$.$ What is the monthly payment on this RAM?b$.$ Generate a loan amortization table?c$.$ What will be the loan balance at the end of the $12-$year term?d$.$ What portion of the loan balance at the end of year $12$ represents principal? What portion represents interest?Problem $3$Five years ago you borrowed $$200,000$ to finance the purchase of a $$240,000$ home. The interest rate on the old mortgage loan is $6$ percent. Payments are being made monthly to amortize the loan over $30$ years. You have found another lender who will refinance the current outstanding loan balance at $4$ percent with monthly payments for $30$ years. The new lender will charge two discount points on the loan. Other refinancing costs will equal $$6,000.$ There are no prepayment penalties associated with either loan. You feel the appropriate opportunity cost to apply to this refinancing decision is $4$ percent.a$.$ What is the payment on the old loan?b$.$ What is the current loan balance on the old loan $($five years after origination$)?$c$.$ What would be the monthly payment on the new loan?d$.$ Should you refinance today if the new loan is expected to be outstanding for five years?Problem $4$You are offered two choices for financing your house, valued at $$200,000,$ as follows:a$.$ A $90$ percent LTV fixed$-$rate $30-$year mortgage at $6\mathrm{.}00$ percent. It will require private mortgage insurance for nine years $($until the loan is reduced to $78$ percent of value$),$ effectively increasing the payment as if the loan were a $6\mathrm{.}75$ percent loan for nine years.