I’ve often wondered how much total money, exactly, I’ll end up paying on a loan set at a particular interest rate. I never took the trouble to find out, though, until I had to pay the kids back their college funds at a set interest rate. Trick is that if money is compounded monthly (meaning they add the interest to your balance at the end of each month), this can be super-hard to deduce—and I was paying the kids back for helping me to pay off our second mortgage, which was compounded monthly (I believe) at an exorbitant interest rate of 11.5% (which I preferred to give them, of course, instead of the -3% they seemed to be getting in their college accounts).
Most of the online formulas I found were too simple, seeming to assume that the money is only compounded once annually, which I don’t think is typically the case. Michael actually once spent time creating a lengthy Excel spreadsheet to calculate compounded interest for him, but I found this formula online and thought I’d share, in case anyone else is wondering how much they’ll owe for a loan that is compounded monthly—or maybe how much money they should end up with from their investments, though I wouldn’t know if those are generally compounded monthly. Remember, though, that payments will alter things; this formula assumes all money is exchanged at once. Nevertheless, I felt compelled to share because it took me hours to decipher the online confusion. Please read through the sample problem before you give up/try it! Here goes…
B=I[1+(r/12)]12n
B is your balance at the end
I is your initial amount
r is your interest rate as a decimal
n is the number of years of a loan
So for a loan at 11.5%, r=0.115
If it’s for two years, n=2, but if it’s 18 months, then n=1.5, right?
And just for practice, if your initial loan was for $2000, and it’s at 3.5% interest, compounded monthly, and you have to pay it back in 20 years, then in twenty years you will owe $4023.40. Remember that as things compound month-by-month, the amounts will be rounded a little, so you’ll end up a few dollars off. If your calculators give you an error code as mine did (even my scientific calculator), you can calculate it on an Excel spreadsheet, which would be entered in this pattern: +I*(1+(r/12))^(12n)
Or, in this case: +2000*(1+(0.035/12))^(12*20)
Good luck figuring out those finances!
Sidenote: The 12s in the formula would change based on how many times per year the compounding occurred, so since there are 12 months in a year, a loan compounded monthly has 12s here. If the loan is compounded daily, the two 12s would be replaced with 365 in each spot. It makes a little difference, but not as much as you might think…
