What is the difference on the total interest payments between a $25$ year $5\mathrm{.}65\%$ fixed rate fully amortizing loan for $$485,000$ and an identical loan taken out for $15$ years?

a$)$ $$186,296\mathrm{.}09$

b$)$ $$101,275\mathrm{.}87$

c$)$ $$137,571\mathrm{.}96$

d$)$ $$96,736\mathrm{.}37$