You own a house, on which you pay a mortgage. Currently you owe 260000 dollars o

Question

You own a house, on which you pay a mortgage. Currently you owe 260000 dollars on your mortgage, and your interest rate is 4.3 percent (this means that every year you pay interest on your debt amounting to 4.3 percent of what you owe). Your mortgage requires you to pay 1600 dollars every month.

Find the general solution to the differential equation Q'= Q(.043)-19.2
Write your answer in the form Q(t)=Ce^(st)+U where s and U are certain constants that you determine, and C is an integration constant that is not yet determined.
Q(t)=?
Use the initial condition to find C.
C=?
How much will you owe after 10 years?

Explanation / Answer

dQ/dt=0.043*Q-1600*12 dQ/(0.043*Q-1600*12)=dt let 0.043*Q-1600*12=p then 0.043*dQ=dp substituting, dp/(0.043*p)=dt ln(p)=0.043*t+c c= a constant p=k*exp(0.043*t) so 0.043*Q-1600*12=k*exp(0.043*t) or Q(t)=23.26*k*exp(0.043*t)+446511.63 at t=0, Q(0)=260000 so k=-8018.556 so final solution Q(t)=23.26*(-8018.556)*exp(0.043*t)+446511.63 at t=10, Q(10)=159795.2504

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