Consider the following four bonds:

I. A $10$ Year bond with a $5\%$ coupon and $7\%$ yield to maturity

II$.$ A $3$ Year bond with a $5\%$ coupon and a $7\%$ yield to maturity

III. A $10$ Year bond with a $3\%$ coupon and a $4\%$ yield to maturity

IV$.$ A $10$ Year bond with a $3\%$ coupon and $7\%$ yield to maturity

If the yield$-$to$-$maturity for all bonds changes by $1\%,$ rank the bonds from lowest percentage change in price

to largest percentage change in price?

a$.$ II$,$ I, IV$,$ III

b$.$ IV$,$ III, II$,$ I

c$.$ I, II$,$ III, IV

d$.$ II$,$ III, IV$,$ I