Homework SourseYou own a house on which you pay a mortgage Currently you ow
You own a house, on which you pay a mortgage. Currently you owe 260,000 dollars on your mortgage, and your interest rate is 4.2 percent (this means that every year you pay interest on your debt amounting to 4.2 percent of what you owe). Your mortgage requires you to pay 1,400 dollars every month.
Q(t)=Ce^(.042*t)+(16.8/.042)
Use the initial Conditions to solve for C:
Q(t)=Ce^(.042*t)+(16.8/.042)
Use the initial Conditions to solve for C:
Solution
let at any time t, money owed by you is Q(t) then dQ(t)/dt=Q(t)*0.042-1400*12 let Q(t)*0.042-1400*12=U(t) then dQ*0.042=dU substituting dU/(U(t)*0.042)=dt so ln(U(t))=0.042*t+c c= a constant U(t)=K*exp(0.042*t) K= a constant now putting Q(t)*0.042-1400*12=U(t) we get Q(t)=23.81*K*exp(0.042*t)+400*1000 at t=0,Q(0)=260000 so K*23.81+400000=260000 so K=-5879.88 so final solution Q(t)=-140000*exp(0.042*t)+400000
