For the following bond,

Par value: $$1,000$

Coupon rate: $8\%$ paid annually

Time to maturity: $3$ years

Interest rate: $2\%$

If the interest rate increases from $2\%$ to $3\%,$ what is the price change due to the convexity?

Select one:

a$.$ $$\mathrm{.}4355$

b$.$ $$\mathrm{.}7002$

c$.$ $$\mathrm{.}5223$

d$.$ $$\mathrm{.}6166$