What if interest is compounded more often than monthly? Some lending institutions compound interest daily or even continuously. (The term continuous compounding is used when interest is being added as often as possible—that is, at each instant in time.) The point of this exercise is to show that, for most consumer loans, the answer you get with monthly compounding is very close to the right answer, even if the lending institution compounds more often. In part 1 of , we showed that if you borrow $7800 from an institution that compounds monthly at a monthly interest rate of 0.67% (for an APR of 8.04%), then in order to pay off the note in 48 months, you have to make a monthly payment of $190.57.
a. Would you expect your monthly payment to be higher or lower if interest were compounded daily rather than monthly? Explain why.
b. Which would you expect to result in a larger monthly payment, daily compounding or continuous compounding? Explain your reasoning. c. When interest is compounded continuously, you can calculate your monthly payment M = M(P , r, t), in dollars, for a loan of P dollars to be paid off over t months using
where r = APR 12 if the APR is written in decimal form. Use this formula to calculate the monthly payment on a loan of $7800 to be paid off over 48 months with anAPR of 8.04%. How does this answer compare with the result?