Hey Hiroi.
Try solving the DE first and then consider how each of the two different loans changes the values of i and p (they will be constants for each loan type).
I sorta need help with this problem. Work shown would be appreciated! And any other form of help =)
Suppose Ms. Lee is buying a new house and must borrow $200,000. She wants a 30-year mortgage and she has two choices. She can either borrow money at 7% per year with no points or she can borrow the money at 6.5% per year with a charge of 3 points. (A "point" is a fee of 1% of the loan amount that the borrower pays the lender at the beginning of the loan. For example, a mortgage with 3 points requires Ms. Lee to pay $6,000 extra to get the loan.) As an approximation, we assume that interest is compounded and payments are made continuously. Let:
M(t) = amount owed at time t (measured in years),
i = annual interest rate, and
p = annual payment.
Then the model for the amount owed is:
dM/dt = iM-p
a)How much does Ms. Lee pay in each case?
b)Which is a better deal over the entire time of the loan (assuming Ms. Lee does not invest money she would have paid in points)?
c)If Ms. Lee can invest the $6,000 she would have paid in points for the second mortgage at 5% compounded continuously, which is the better deal?
Thank you so much if you can help me through this problem =)
The differential equation is separable. Your independent variable is t and your dependent is p but you can get a dp/f(p) = dt*g(t) and integrate boths sides.
Hint: for this case f(p) = iM - p (use the other information to get g(t) and be aware that g(t) can be a constant independent of t as a special case).