Belinda Johnson$$s parents and maternal grandmother have combined their finances and presented Harry and Belinda with $$50,000$ cash gift to use to purchase a home. The Johnsons have shopped and found a house in a new housing development that they like very much. They could either borrow from the developer or obtain a loan from one of three other mortgage lenders. The financial alternatives and data for the home are summarized in the table below.

$($a$)$

Which plan has the lowest total up$-$front costs? The highest?

$($b$)$

What would be the full monthly payment for PITI and PMI for each of the options?

$($c$)$

If the Johnsons had enough additional cash to make the $20$ percent down payment, would you recommend lender $1$ or lender $2?$ Why?

$($d$)$

Assuming that the Johnsons will need about $$3,000$ for moving costs $($in addition to closing costs$),$ which financing option would you recommend? Why?Price: $$290,000.$ Developer A will finance the purchase with a $10$ percent down payment and a $30-$year, $5$ percent ARM loan with $2$ interest points. The initial monthly payment for principal and interest is $$1401\mathrm{.}10($$$261,000$ loan after the down payment is made; $261*$ $$5\mathrm{.}3682).$ After one year, the rate rises to $5\mathrm{.}5$ percent, with a principal plus interest payment of $$1481\mathrm{.}94.$ At that point, the rate can go up or down as much as $2$ percent per year, depending on the cost of an index of mortgage funds. There is an interest$-$rate cap of $5$ percent over the life of the loan. Taxes are estimated to be about $$3,800,$ and the home$-$owner's insurance premium should be about $$1,800$ annually. A mortgage insurance premium of $$88$ per month must be paid monthly on the two $10$ percent down options. Figure out the best option for them, and explain why.

$\backslash$table$[[$Home: Price, $$290,000$; Taxes, $$2,800$; Insurance, $$1,700],[,$Developer A$,$Lender $1,$Lender $2,$Lender $3],[$Loan term and type,$30-$year ARM$*,30-$year Con ${?}^{},15-$year Con,$20-$year Ren$],[$Down payment,$$29,000,$$$58,000,$$$58,000,$$$29,000$