The term structure of effective annual yield rates for zero coupon bonds is given as follows: $1-$ and $2-$year maturity, $10\%$; $3-$ and $4-$ year maturity, $12\%.$ Find the price of a $4-$year bond with face amount $100,$ and annual coupons at rate $5\%.$ The first coupon will be paid in one year. Answer should be $78\mathrm{.}97.$