Question $9$

$1pts$

A borrower is looking to finance $90\%$ of the purchase price on a house he is buying. His lender proposes a two$-$loan package financing as the follows.

$1$st mortgage: $80\%$ LTV$,25yr,5\%$

$2$nd mortgage: $10\%$ LTV$,25$yr$,9\%$

But the borrower insists to have one $90\%$ LTV $($loan$-$to$-$value$)$ mortgage. What should the interest rate be on the $90\%$ loan so that the lender will receive same yield regardless which option the borrower chooses? $($Hint: the actual purchase price does not affect the results$)$

$6\mathrm{.}69\%$

$5\mathrm{.}48\%$

$6\mathrm{.}42\%$

$5\mathrm{.}12\%$