Consider the following two bonds:

Bond A:

$-$ Term to maturity: $10$ years from today

$-$ Face value: $$1,000$

$-$ Annual Coupon rate: $6\%$

$-$ Number of payments per year: $1$

Bond B:

$-$ Term to maturity: $20$ years from today

$-$ Face value: $$1,000$

$-$ Annual Coupon rate: $10\%$

$-$ Number of payments per year: $1$

a$)$ Compute the price for each bond. The current market interest rate for the bond is $8\%.$ Assume that YTM of each bond equals the current market interest rate. Then make a table comparing the bond prices when the YTM varies from $1\%,2\%..\mathrm{.}17\%.$

b$)$ Compute duration and modified duration for each bond.

c$)$ Use $($modified$)$ duration to estimate the percentage change of price for each bond if the YTM increases from $8\%$ to $12\%.$

$*$please show excel formula