why did we use a monthly interest factor of .004868 or .4868% monthly rate instead of .005 or .5% monthly rate to solve the problem which had a stated APR of 6%?

Example 5.1 Valuing Monthly Cash Flows ( 3 of 6) How can we picture the timeline? SECOND QUESTION Month Cash fl That is, we can view the savings plan as a monthly annuity with 10x 12=120 monthly payments. We have the future value of the annuity ($100,000), the length of time (120 months), and we will have the monthly interest rate from the answer to the first part of the question. We can then use the future value of an annuity formula (Eq. 4.6) to solve for the monthly deposit. Example 5.1 Valuing Monthly Cash Flows (4 of 6 ) Execute SECOND QUESTION - CONT'D - To determine the amount to save each month to reach the goal of $100,000 in 120 months, we must determine the amount C of the monthly payment that will have a future value of $100,000 in 120 months, given an interest rate of 0.4868% per month. - Now that we have all of the inputs in terms of months (monthly payment, monthly interest rate, and total number of months), we use the future value of annuity formula from Chapter 4 to solve this problem: Example 5.1 Valuing Monthly Cash Flows (5 of 6 ) ANSWER TO SECOND QUESTION FV(annuity)=Cr1[(1+r)n1] We solve for the payment C using the equivalent monthly interest rate r=0.4868%, and n=120 months: C=r1[(1+r)n1]FV(Annuity)=0.0048681[(1.004868)1201]1=$615.47permonth. - NOTE: Why didn't we use the monthly interest factor of .061/12=.005 or .5% monthly rate? Example 5.1 Valuing Monthly Cash Flows (3 of 6) Execute FIRST QUESTION - From Eq. 5.1, a 6% EAR is equivalent to earning (1.06)1/21=0.4868% per month. The exponent in this equation is 121 because the period is 121 th of a year (a month). - Or 1.06 to the 1/12 power =1.0048681=.004868 why did we use a monthly interest factor of .004868 or .4868% monthly rate instead of .005 or .5% monthly rate to solve the problem which had a stated APR of 6%