How does APR work on a loan?
In: 3
The “annual percentage rate” is *roughly* how much extra you’d owe if you made zero repayments for a year. Of course, that never happens, because the loan agreement will have you agreeing to make regular payments.
Instead, the bank’s computer turns the *annual* interest rate into a *daily* interest rate by dividing by 365 (or 366). Then, each day, they look at the balance, and tally up the interest you owe on the balance that day. After (say) a month, they charge your loan account the accumulated interest.
For example, suppose your loan was at 7.3% APR. That’s a daily rate of 0.02%. If you owed $10000, the bank would be noting every day that you owe them an extra $2, though they probably don’t actually *charge* you that until the end of the month.
If you paid $1000 on day 15, then your balance is $9000, so now you only owe an extra $1.80 per day. On day 30 they debit your loan account the accumulated interest: 15 x $2 + 15 x $1.80 = $57. Now your balance owing is $9057.
Fees are not counted in the APR, though some countries force banks to publish a “comparison rate”, which is the “effective” APR including all the fees, for a “typical” mortgage.
To understand the APR (annual percentage rate) you should also understand the EAR (effective annual rate.)
The APR is how banks typically state the rate to the borrower, for example, 6%. It is the minimum interest that a borrower would pay if they took out a loan at the start of the year, the bank calculated the interest to be paid at the end of the year, and the borrower pays back the loan with interest at the end of the year. When interest is only calculated once in a year then the APR = EAR.
However, banks will often calculate interest more often than once a year. In this case they will still state the APR (e.g APR =6%) and will also state how frequently interest is calculated (e.g. **semi-annually,** or **twice** per year.) Because there are **2** periods that interest is calculated in the interest in each period is 6% / **2** = 3% each period.
In this case, EAR = (1 + 3%) ^ **2** -1 = 6.09%
Due to the effect of compounding the EAR > APR if interest is calculated more than once per year.
In summary:
– APR is the amount of interest quoted by the bank.
– EAR takes into consideration how frequently interest is calculated and can tell you the actual % interest that would be paid from the borrower to the lender.
– If you were to compare two loans for which one paid the highest interest you’d compare EARs.
Your credit score and other factors determine how likely you are to pay back your money on time. The better this is, the less interest (% extra money) you have to pay on top of the amount you borrowed.
APR is the yearly % interest. However, it typically is compounded (broken up) throughout the year (usually monthly), so the actual effective % change is different, called APY.
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I’ll actually use a saving account that you don’t contribute to as an example because it’s easier.
Let’s say you open up a saving account with $10,000 and a 12% APR compounded monthly; this gives you 1% each month (12%/12 months).
Month 0: $10,000
Month 1: $10,100
Month 2: $10,201
Month 3: $10,303.01
….
Month 12: $11,268.25
$11.268.25 is 12.68% more than $10,000, so it’s a 12.68% APY achieved from a 12% APR compounded monthly (if it was compounded daily then the amount would be even more).
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Let’s make a loan scenario now though:
$10,000 to be paid back in 1yr with a 12% APR compounded monthly.
With 0% interest it would be ~$833.33 every month, with this interest it would be ~$888.49.
If you are allowed to do extra/pre payments and without penalty, for sure do that. Because in Month 1 the amount of the $888.49 that you’d be paying has $100 being just the interest and $788.49 being for the amount borrowed, whereas in Month 12 it is only $8.80 on interest and $879.69 on the amount borrowed.
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