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 bankkusd per month. LetS(t), measured in usd, be the balance due on the loan at any timet, measured in years.

(a) Write a differential equation to calculate the amount of loan left to be

paid.

(b) Solve forS(t).

(c) If the worker wishes to pay off the loan in 5 years, find the value of the monthly paymentkusd.

(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.......