The table below summarises some information from the fixed$-$income market: Bond Maturity $($years$)$ Coupon rate $(\%)$ Yield $(\%)$

A $5\mathrm{.}502\mathrm{.}5$

B $2\mathrm{.}542$

a$)$ Calculate the duration and the modified duration for the two bonds.

b$)$ Which of the two bonds will have the smallest price change for a given change in the interest rate? Give a short explanation.

c$)$ If a fund manager invests $($for face value$)$ NOK $10$ million in bond A and $($for face value$)$ NOK $16$ million in bond B$,$ what will the duration of the portfolio be$?$