A person initially places $1000 in a saving account that pays interest at the rate of 1.1% compounded continuously . Suppose the person arranges for $20 per week to be deposited into the savings account.

a) Write a differential equation for P(t), the amount on deposit after t years (assume weekly deposits is close enough to continuous deposits)

b) Find the amount on deposit after 5 years?

I was already given the answer to a.) as dP/dt= .011P+1040 and b) as $6,402.20 but I'm not sure how these answers were gotten

I know that the 1040 represents 20 dollars per week and the .011 represents 1.1% over the course of the whole year but I'm not sure where P came in or how to start B at all