CALC Help: You own a house, on which you pay a mortgage?

Currently you owe 260,000 dollars on your mortgage, and your interest rate is 4.8 percent (this means that every year you pay interest on your debt amounting to 4.8 percent of what you owe). Your mortgage requires you to pay 1500 dollars every month.
A. How much money do you pay to your mortgage company every year (in dollars)?

$18,000

B. Let Q(t) denote the amount of money you owe after t years, MEASURED IN THOUSANDS OF DOLLARS. Assuming that the payments and interest all take place continuously, write down a differential equation satisfied by Q(t).

Q′ = .048Q-18

C. Find the general solution to the differential equation from part B. Write your answer in the form Q(t)=Cest+U where s and you are certain constants that you determine, and C is an integration constant that is not yet determined.

Q(t)=

D. Use the initial conditions to solve for the constant C:

C=

E. How much money will you owe still owe on the mortgage after 10 years? Give your answer in dollars, and round to the nearest cent.

amount owed is ________ dollars.

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