Problem $5.$ A $1000$ par value bond pays annual coupons of $80.$ The bond is re$-$ deemable at par in $30$ years, but is callable anytime from the end of the $10$th year at $1050.$

I Based on her desired yield rate, an investor calculates the following potential purchase prices, P:

$$ Assuming the bond is called at the end of the $10$th year. P $=957$

$$ Assuming the bond is held until maturity. P $=897$

The investor buys the bond at the highest price that guarantees she will receive at least her desired yield rate regardless of when the bond is called.

The investor holds the bond for $20$ years, after which time the bond is called.

Calculate the annual yield rate the investor earns.