You purchased two bonds a $10$ year Treasury that has a $2\%$ coupon and a $20$ year Treasury that has a $5\%$ coupon three years ago. Both securities pay coupons semiannually. You purchased the $10$ year and $20$ year bonds with YTMs of $4\mathrm{.}25\%$ and $4\mathrm{.}65\%,$ respectively. Since purchasing the bonds the yields have decreased, by $50$ basis point for you $10$ year bond and $35$ basis point for your $20$ year bond. Calculate the holding period return for both bonds.

Please show all of your work for credit.