Question $7$:

A $100,000$ loan is to be repaid by $30$ equal payments at the end of each year. The outstanding balance is amortized

at $4\%.$

In addition to the annual payments, the borrower must pay an origination fee at the time the loan is made. This fee is

$2\%$ of the loan but does not reduce the loan balance.

When the second payment is due, the borrower pays the remaining loan balance.

Determine the yield to the lender considering the origination fee and the early pay$-$off of the loan. $[$SOA $\frac{5}{86}$ #$7]$

$($A$)4\mathrm{.}9\%$

$($B$)5\mathrm{.}0\%$

$(1)5\mathrm{.}1\%$

$($D$)5\mathrm{.}2\%$

$($e$)5\mathrm{.}3\%$