Last year a firm issued $20-$year, $8\%$ annual coupon bonds at a par value of $$1,000.$

a$.$ Suppose that $1$ year later the going market interest rate drops to $6\%.$ What is the

new price of the bonds, assuming they now have $19$ years to maturity? $($$$1,223\mathrm{.}16)$

b$.$ Suppose that $1$ year after issue, the going market interest rate is $10\%($rather than

$6\%).$ What would the price have been? $($$$832\mathrm{.}70)$

Why do the prices of fixed$-$rate bonds fall if expectations for inflation rise?