A person initially places $1,000 in a savings account that pays interest at the rate of 1.1% per year compounded continuously. Suppose the person arranges for $20 per week to be deposited automatically into the savings account.
(a) Write a differential equation for P(t), the amount on deposit after t years (assume that “weekly deposits” is close enough to “continuous deposits” so that we may model the balance with a differential equation.)
(b) Find the amount on deposit after 5 years.
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