A $1000$ par value bond with coupons of $6\%$ payable annually is redeemable at par in $20$ years, but it is callable any time from the end of

the $10$th year at $1030.$

Based on an investor$$s desired yield rate, the investor calculates the

following potential purchase prices:

Assuming the bond is called at the end of the $10$th year, the purchase

price is $879\mathrm{.}69.$

Assuming the bond is held until maturity, the purchase price is $803\mathrm{.}64.$

The investor buys the bond at the highest price that guarantees that

the investor will receive at least the desired yield rate.

The investor holds the bond for $15$ years, at which time the bond is

called. Calculate the annual effective yield rate the the investor earns.