Suppose you obtain a $250,00 conventional mortgage at an annual interest rate of 4%.

(a) If its a 30 year mortgage, what is your monthly payment?

(b) If its a 15 year mortgage, what is your monthly payment? (Usually, a shorter term mortgage would have a better rate, but lets ignore that.)

(c) Some would think that the payments for the 15 year mortgage would be roughly double the payments for the 30 year mortgage. Does that seem to be the case?

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(d) If 4% compounded daily would give an effective annual rate of (1 + .04/365)^(365)-1, what would the effective annual rate compounded continuously be? In other words, what is limn(1 + .04/n)^n 1?