Suppose you make a deposit of $P into a savings account that earns interest at a rate of 100 r% per year. 

a. Show that if interest is compounded once per year, then the balance after t years is B(t) = P(1 + r)^t.

b. If interest is compounded m times per year, then the balance after t years is B(t) = P(1 + r/m)^mt. For example, m = 12 corresponds to monthly compounding, and the interest rate for each month is r/12. In the limit m→∞, the compounding is said to be continuous. Show that with continuous compounding, the balance after t years is B(t) = Pe^rt.