Suppose you purchase a zero coupon bond with face value $$1,000,$ maturing in $25$ years, for $$180.$ If the yield to maturity on the bond remains unchanged, what will the price of the bond be $5$ years from now?

a$.$ $$253\mathrm{.}64$

b$.$ $$287\mathrm{.}52$

c$.$ $$310\mathrm{.}91$

d$.$ $$380\mathrm{.}58$

e$.$ $$500\mathrm{.}00$ How to solve in calculator also how to find rate for this question?