Annuities. Please show step by step. Answer is D$.$

Mat takes out a loan for a car for $$35,000.$ He must make $16$ annual payments of $$4,000.$ For the

first $7$ years the interest rate is $8\%,$ what is the annual effective interest rate for the last $9$ years?

a$.)\mathrm{.}115$

b$.)\mathrm{.}242$

c$.)\mathrm{.}082$

d$.)\mathrm{.}087$

e$.)\mathrm{.}468$