I am trying to calculate the amount of time it will take for me to pay off my student loan with a fixed monthly payment amount. I have been trying to solve this problem for a few days now to no avail. Using the information i have gathered from the internet and the various calculators online for calculating the monthly payment. I cant figure out the formula that is being used. Everywhere it states that student loans are simple interest but it seems like this is not the full truth.
So far iv been able to get "close" to the numbers that they provide by using this formula.
A = P ( (r/365) * (Q * (t*365) ) ) Simplified A = P (rQt) Total amount for t years = A + P Solve for t t = PrQ/A
where: A = monthly payment P = principle r = percent/100 t = time in years or * 12 for months Q = (2.729/5)*365t ~= 199.219 which has something to do with the amount of days you attend a year of schooling but from my research this number varies very slightly based on time and rate. This includes fall semester, spring semester, winter semester, and summer semester but excludes days off. My thinking is because this loan is given out specifically for those time periods only and not to be used throughout a full 365 days like an auto loan.
So my question is what is the equation for calculating how long it will take to pay off a student loan with (P) amount, (r) interest and (A) monthly payment amount? It seems as though this will not be an algebraic equation but a calculus one instead. Here is one the calculators i have used so far out of maybe 10 https://smartasset.com/student-loans/student-loan-calculator