$1.$ You have a large position in $2$ bonds with similar credit risk. i$.$de$.,$ ignore credit risk$)$ Bond A is priced at par yielding $6\%$ with $20$ years to maturity. Bond B has $20$ years to maturity, coupon of $7\%,$ and yield of $6\%.$ Assume a face value of $100$ for both bonds and annual compounding.

a$.$ Without making detailed calculations, can you guess which bond has a higher duration?

b$.$ Now calculate the durations of these bonds using excel. Where you right?