A worker borrows usd 550,000 at an annual interest rate of 6% to purchase a house from a bank. Suppose he make an arrangement to pay the bank k usd per month. Let S(t), measured in usd, be the balance due on the loan at any time t, measured in years.
(a) Write a differential equation to calculate the amount of loan left to be
paid.
(b) Solve for S(t).
(c) If the worker wishes to pay off the loan in 5 years, find the value of the monthly payment k usd.
(d) What is the total amount paid over the life of the loan and hence find the
total interest payment made?
i know that the de :
S(t) = S_0*e^{rt}
dS/dt= r*S_0*e^{rt} = r*B(t)
IS THIS CORRECT FOR Q (a) and (b)
But from here how can i know the total paid over the life of the loan .... and the total interest payment????
is that occur when set t ----> infinity?????
plz help me.......