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 3.3 percent (this means that every year you pay interest on your debt amounting to percent of what you owe). Your mortgage requires you to pay 1900 dollars every month.
B) Let Q(t) denote the amount of money you owe after t years. Assuming that the payments and interest all take place continuously, write down a differential equation satisfied by Q(t).
Q\'=??
B) Let Q(t) denote the amount of money you owe after t years. Assuming that the payments and interest all take place continuously, write down a differential equation satisfied by Q(t).
Q\'=??
Solution
Let Q(t) denote the amount of money you owe after t years. dQ(t)/dt=r*Q(t)-1900*12=0.033*Q(t)-22800 dQ(t)/[0.033*Q(t)-22800]=dt initial condition,Q(0)=260,000 dollars integrating Q(t)=c*exp(0.033*t)+690.9*10^3 Q(0)=260,000 so c=-430.9 *10^3. hence Q(t)=-430.9 *10^3*exp(0.033*t)+690.9*10^3
