You plan to purchase a home in $6$ years. The goal is to have $$L$ as a down payment. In order to meet that goal, you invest in two zero coupon bonds. One zero coupon bond for face amount A matures in $4$ years. A second zero coupon bond for face amount B matures in $8$ years. You choose amounts A and $B$ such that the ability to make the down payment in $6$ years is immunized from changes in interest rates.

Assume the current force of interest is $ln(1\mathrm{.}05).$ Define $P()$ as the price of the assets minus the liabilities at $.$

When immunizing your portfolio, you calculated $)=(ln(1\mathrm{.}05)$ to equal to the following:

$)=(ln(1\mathrm{.}05)$

Calculate $P(ln(1\mathrm{.}07))-P(ln(1\mathrm{.}05)).$

$9$

$19$

$29$

$39$

$49$