If one wants to borrow $55,000 from the local bank and can only afford to make monthly payments of $1,120 but no more. Assumming monthly compounding, what is the highest rate you can afford on a 60-month APR loan?
Any help will be much appreciated.. please show work as it will help me figure out how to calculate these type of problems…Thank You in advance
How To Calculate Annuity Present Values?? Answer= 10 Points?
11
Nov
Allen W
November 11, 2009 at 2:00 pm
Let x be the monthly interest rate, then $55,000 * (1+x)^60 = $1120 + $1120 (1+x) + $1120 (1+x)^2 + …… + $1120 (1+x)^(60-1), where on the left side of the equation is the amount of money that $55,000 will become at the end of 60 months at monthly interest rate x, and on the right side is the sum of the annuity, where first term is the last payment at the end of the 60-month period, the second term is the 59th payment that earns 1 month’s interest at monthly interest rate of x, and so forth, to the last term which represents the first payment plus 59 months worth of interest.
It is not easy to solve for x manually. You can use an annuity calculator or look up in an annuity table to find the interest rate. I used http://www.uic.edu/classes/actg/actg500/… which gave me a month interest rate of 0.681838%, or 8.182% compounded monthly, which is the highest rate you can afford.