Compound Interest. If P(t) is the amount of dol- lars in a savings bank account that pays a yearly interest rate of r% compounded continuously, then dP dt 100 t in years. Assume the interest is 5% annually, P(0) = $1000, and no monies are withdrawn. (a) How much will be in the account after 2 yr? (b) When will the account reach $4000? (c) If $1000 is added to the account every 12 months, how much will be in the account after 3 yr