3. (practice with calculus) Consider an annuity that pays C per year with m payments per year for T vears. Then each payment would have size C. Let t, be the time (date) of payment j. Suppose (for simplicity and without loss of generality) that the present time is t-0. The continuous time interest rate is r. The present value of the payment at time t, is -rt, 1 TL (a) Write a formula for the total present value of the annuity, of the form The number of pavments in total is n-mT = (payments per year) (number of years). (b) Write an explicit formula for Vm Hint: The sum from part (a) is a geometric series, once you take out the common factor. It helps to write a formula for tj in terms of j and m. The geometric series formula is S(z)-z + z2 + + z-(z-zn+1)/(1-z)