Krishna buys an n$-$year $1,000$ bond at par. The Macaulay duration

is $6\mathrm{.}85$ years using an annual effective interest rate of

$8\%.$Calculate the estimated price of the bond, using first$-$order

macaulay approximation, if the interest rate drops to $7\mathrm{.}4\%.971\mathrm{.}32$

$985\mathrm{.}62998\mathrm{.}671038\mathrm{.}901204\mathrm{.}56$

Krishna buys an $n-$year $1,000$ bond at par. The Macaulary duration is $6\mathrm{.}959$ using an annual effective interest rate of $6\mathrm{.}2\%.$ Calculate the estimated price of the bond, using the first order Macaulay approximation, if interest rates rises to $6\mathrm{.}5\%$