Jack bought a $4\%$ coupon bond three years ago for $$950.$ The bond pays interest semiannually and has a face value of $$1200$ with a maturity date of $10$ years $($starting from the time of purchase$).$ Jack just sold the bond to Adam. If Adam negotiated for a $3\mathrm{.}53\%$ per year return for the rest of the bond period of $7$ years, calculate:a$.$ How much Adam bought the bond for?b$.$ Jack's rate of return on the bond.