If I borrow 100k at 5% interest, and to be paid back in 5 years, why is it not that case that I just pay 21k per year and would have paid 105k after 5 years? I heard that if I pay back a little extra every year, it will help to go pay off the interest first, what does that mean? If I owe a set amount of money on fixed interest, how can the total amount change?
In: 4
The ELI5 answer is that you pay interest on unpaid interest, which is significantly more than you might think.
A more detailed answer:
First, interest is usually a stated rate per year. So 100K borrowed at 5% per year would require a much larger payoff than 105K in five years. If the full amount of the loan is to be paid at the end of 5 years in one payment, it will be $127,628.16; this is different from the 105K payoff you hypothesized. The payoff can be calculated by the formula:
Future Value = Present Value * (1 + interest rate)^(Number of years)
Note: 5% is equivalent to the number 0.05
The present value is the borrowed amount and the future value is what you will pay back.
$127,628.16 = $100,000 * (1 + 0.05)^5
The reason this amount is different from the $105k you hypothesized is that you pay a fee (interest of 5% per year) on the money you owe and each year you owe a little more because you have not paid the interest that accumulates each year. At the end of the 5 year loan, you pay back your original debt (principal) and the sum of all the interest charges that have accumulated (interest). Essentially you owed interest on the unpaid interest that accumulated each year. That is what makes the whole system seem wonky. Please note that I am explaining the “simple” case where you borrowed money and made one payment at the end of the 5 year loan.
Mortgages are paid back in installments. There are two parts to your payments, the interest (the “fee” for borrowing) and the principal (what goes toward paying off your debt). With each payment some goes toward principal and then some goes to pay the interest on the outstanding debt. After a payment the next payment will have more going towards principal and less towards interest. The first payment will be almost 100% interest and the last payment will be almost 100% principal. Calculations for this are more detailed. I won’t get into them here…
In a somewhat idealized world, and from a borrowers perspective, if I want to make an extra payment on my mortgage I would like that to go directly towards my outstanding principal. That is the most effective way to lower the accumulated interest over the life of the loan and correspondingly the quickest way to pay off the loan. Why would I want to pay my bank interest (the fee for lending me money) early? I want to pay my principal early.
In practice, I have found that the only way my bank credits any extra payments towards principal is to conspicuously write “principal only” in the memo line of the check I write them. And then to call them after they “accidentally” credit my early payment towards interest I don’t owe yet, and insist they correct their mistake. After a few iterations of this they get the idea. Sort of a “they know, that I know, that they know” situation.
I took a class years and years ago that taught me this kind of stuff. The math is not hard and it changed the course of my life. They should teach it in high school.
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