In Section 3.9, we use the formula to derive the monthly interest rate from a...

In Section 3.9, we use the formula

to derive the monthly interest rate from a given annual interest rate, where MR is the monthly interest rate and AR is the annual interest rate (expressed in a fractional value such as 0.083). This annual interest rate AR is called the stated annual interest rate to distinguish it from the effective annual interest rate, which is the true cost of a loan. If the stated annual interest rate is 9 percent, for example, then the effective annual interest rate is actually 9.38 percent. Naturally, the rate that the financial institutions advertise more prominently is the stated interest rate. The loan calculator program in Section 3.9 treats the annual interest rate that the user enters as the stated annual interest rate. If the input is the effective annual interest rate, then we compute the monthly rate as

MR = (1 + EAR)^1/12 -1

where EAR is the effective annual interest rate. The difference between the stated and effective annual interest rates is negligible only when the loan amount is small or the loan period is short. Modify the loan calculator program so that the interest rate that the user enters is treated as the effective annual interest rate. Run the original and modified loan calculator programs, and compare the differences in the monthly and total payments. Use loan amounts of 1, 10, and 50 million dollars with loan periods of 10, 20, and 30 years and annual interest rates of 0.07, 0.10, and 0.18 percent, respectively. Try other combinations also. Visit several websites that provide a loan calculator for computing a monthly mortgage payment (one such site is the financial page at www.cnn.com). Compare your results to the values computed by the websites you visited. Determine whether the websites treat the input annual interest rate as stated or effective.