# Can you calculate an answer to this question about a loan with interest?

The two things I don’t know, which you would usually know in a case like this, are the original loan amount and the length of time over which the loan is supposed to be paid off.

As of right now, the current balance is 6069.24

The monthly payments are 281.11

Out of the latest payment, \$19.46 of that was interest, the rest principal.

The APR is 3.4%.

And what I’m trying to figure out is how much more interest I will pay over the life of the loan. (To figure out how worth it it would be to pay this thing off immediately.)

I can find out the missing information tomorrow, so nbd, but I was curious to see if there’s a way to calculate it out without that information. Is there sufficient information here?

I think not because that balance and monthly payment amount are compatible with any conceivable loan term, given the right starting balance when the loan was originally made. But I can’t quite see whether nailing down the interest rate somehow zeroes in on a particular loan term given the other info.

Well… that’s what I’ve got.

I do know the original loan amount was in the \$14,000s.

And I believe the thing has about two years to go.

If you don’t want to build it in Excel, there are a few websites where you can approximate. Try this with your remaining balance and 22 months. Then click the show/recalculate amortization table button. You’ll then have to add up the interest column. There are some options for seeing what happens with extra payments.

If you poke around, some other websites might sum up the interest payments for you, but a spreadsheet might be faster. https://www.google.com/search?q=amortization+schedule+excel
Keep in mind this discounts the time value of money (i.e. money paid now costs more than money paid tomorrow). At a piddling 3.4% APR, there are many folks who would rather divert extra funds to their investment account than to the loan.

If you had a loan of \$14,057.30 with an interest rate of 3.4% and a term of 4.5 years (info not given by OP), the monthly payment (12 times a year) could be your \$281.11 and over the life of the loan you’d pay \$15,179.94, or \$1,122.64 in interest, depending on how compounding was done.

I’m running out the door right now, but it’s certainly doable. You know how much you paid in interest on the last payment, and you know the interest rate. Between those, you can determine the current balance, and hence everything else.

You’ve actually given more information than is needed to determine the remaining time on the loan: The interest rate determines how much of the last payment was interest and vice versa. On the other hand, that interest rate and interest payment don’t seem to match.

Never mind. What you need is a time value of money calculator, of which there are many on the Web, like this one chosen at random. Enter the present value as positive, the payment as negative (or the other way around, it doesn’t matter in this case), the future value as 0, and the interest rate. Choose monthly compounding for a loan with monthly payments. Press the “Periods” button and it will calculate the number of remaining periods for you.

From the information given, you can’t determine the original amount or how long the loan has been in existence. You could extend backwards any length of time you like.

The proportion of each payment that goes to interest decreases each month. I should have mentioned that.

You didn’t have to mention that. That’s always true.

If you have a balance of \$6069.24, a monthly payment of \$281.11, and an interest rate of 3.4%, you have 1.859 remaining years worth of payments (about 22 months), and a total remaining interest to be paid of \$202.11. This according to my “mortgage calculator” app on my phone.

This ignores the original loan amount and the original term of the loan, but those don’t really matter. The interest already paid is, well, already paid. All that’s left to worry about is the interest you can still avoid, the \$202.11.

Specifically, if your balance is \$B at the beginning of a month, the interest portion of your payment at the end of the month is the interest owed for having borrowed \$B for one month. With the interest rate you gave, that should be B x 0.034/12. As you decrease \$B each month, the interest part of the payment goes down as well. I just can’t make that square with the payment amount and interest amount you gave.

But isn’t this incompatible with what Topologist said, namely that the interest rate and the amount that went toward interest determine the length of the loan? If the interest proportion changes over time, won’t different rates of change determine different loan lengths?

Probably I am just failing to know something about how the proportion that goes to interest is calculated. Until recently I just let this all happen under the hood so to speak.

ETA: Based on Topologist’'s last post, it was indeed the case that there was something I didn’t know about how the proportion-going-to-interest was determined.

I’m still puzzled why he can’t make the numbers come out to what I said, though. It is definitely 3.4 interest, the balance is as I said, and the amount that went to interest is definitely what I said.

Is it close? The numbers I gave are almost certainly accurate–the only source of error I can think of is maybe I gave a loan amount and an amount-paid-toward-interest that were a month apart.

But in any case, you guys are basically saying I can just take the present total owed and present interest rate etc and just treat it as a fresh loan, right?

That’s the only way to look at it, if you are interested in what options you still have. The only reason to look at past values is if you want to play “I could have…” games. Those are not recommended.

The term in microeconomics for money already spent is “sunk costs.” If you can’t get them back (and generally you can’t), they are not included in calculations, because they don’t matter any more.

I’m assuming that the \$6069.24 balance was after the payment of \$281.11 that included interest of \$19.46. That means that the principal before the payment was 6069.24 + (281.11 - 19.46) = \$6330.89. One month’s interest on that amount, at 3.4%, would be 6330.89 x 0.034/12 = \$17.94.

Trying to calculate it the other way, if the interest payment was \$19.46, then the interest rate would have been 19.46/6330.89 x 12 = 3.689%.

This is what’s confusing me about the numbers.

The reason less of your payment goes to interest each month is that each month, you accrue less interest. Look at it this way: In a given month, the interest that accrues is your loan balance times your monthly interest rate. Your payment is always somewhat bigger than that. Some of it goes to pay off the interest that accrued that month, and the rest pays down a little of the principal. Since you just paid down a little of the principal, you will accrue *less *interest the following month, so more of your payment is free to go to principal. Loans with constant payments (the standard method) always work like that.

Or, as in my OP, you may be under the mistaken impression that the total length of the loan has something determinative to do with how much longer the loan has to go, even given all the information I’d provided. As mentioned previously–I thought something more complex was going on with the way the amount paid to interest shrinks each month.

I think I gave numbers that were a month off from each other–i.e., an amount paid to interest from one month, and a loan balance from the previous month.

If the interest payment was \$19.46, then the balance just before that payment would have been 19.46/(0.034/12) = \$6868.24. The numbers could be right, but would have had to have been from several months apart.

The total length of the loan is not particularly important when we already have the monthly payment, interest amount, and interest rate, at least when we phrase the question as relating to the current balance and remaining payments. The interest amount and interest rate let us calculate the current balance, and the size of the payments tell us how much longer the loan has left.

We’d only need the length of the loan in order to calculate past information about the loan, like lifetime interest. That’s because as we go back in time, we can keep calculating larger loans with longer lives - for example, we could project the loan back to have a 5-year auto loan or a 30-year mortgage. As others have said, this past information might be of general interest to you, but it’s not particularly useful for decision making; you can’t change what’s already been spent.

Topologist, one possible source of confusion is that the 3.4% figure isn’t the interest rate; it’s the APR. The APR basically takes into account compounding over the course of one year, while the interest rate doesn’t. Or to put it another way, an APR is a finite difference, while an interest rate is a derivative.

I don’t think that actually resolves the confusion, though, since an APR will always be higher than an interest rate.