📈 Interest Rate & APY Calculator
Calculate simple and compound interest returns, total interest earned, and effective annual yields.
Nominal rate, APR and APY, and why three numbers describe one loan
A single borrowing or saving arrangement can be quoted three different ways, and the three numbers will not match. The nominal rate is the headline. The APY adds the effect of compounding. The APR adds the effect of fees. Comparing a nominal rate against an APR is how people end up choosing the more expensive product.
Nominal rate to APY
The nominal rate ignores how often interest is credited. Once you account for it:
APY = (1 + r/n)n − 1
A 6% nominal rate compounded monthly is an APY of 6.168%. Compounded daily it is 6.183%. The gap widens with the rate: at 18%, monthly compounding turns the nominal figure into 19.56%, which is why credit card debt grows faster than the advertised rate suggests.
| Nominal | Quarterly | Monthly | Daily |
|---|---|---|---|
| 3% | 3.034% | 3.042% | 3.045% |
| 6% | 6.136% | 6.168% | 6.183% |
| 12% | 12.551% | 12.683% | 12.747% |
| 18% | 19.252% | 19.562% | 19.716% |
| 24% | 26.248% | 26.824% | 27.115% |
APR: the rate with the fees folded in
APR expresses the total cost of credit as an annual percentage, including origination fees, points and mandatory charges. Its purpose is comparability. On a $200,000 thirty-year mortgage, a 6.0% rate with $4,000 of fees carries an APR of about 6.18%, and a 6.1% rate with no fees carries an APR of 6.10%. The second loan has the higher rate and is the cheaper one.
APR assumes you keep the loan for the full term. If you expect to move or refinance within a few years, a loan with low fees and a slightly higher rate usually wins, because the fees are spread over far fewer years than the APR calculation assumes.
Finding the rate you are actually paying
Sometimes you know the amount, the payment and the term but not the rate, which is common with dealer finance and buy-now-pay-later offers. There is no closed-form solution for the rate in the annuity formula, so it has to be found numerically; the calculator does this by iteration.
It is worth doing. An offer of "$1,200 over 12 monthly payments of $115" sounds modest. The total repaid is $1,380, which on a reducing balance works out at about 26.6% APR.
Real rate versus nominal rate
Inflation erodes the value of interest earned. The exact relationship, known as the Fisher equation, divides rather than subtracts:
real rate = (1 + nominal) / (1 + inflation) − 1
A savings account paying 4.5% while inflation runs at 3.2% gives a real return of 1.26%, not 1.3%. The shortcut of subtracting is close enough at low rates and badly wrong at high ones: 40% nominal against 35% inflation is a real return of 3.7%, not 5%.
A worked example
Two savings accounts. Account A pays 4.40% compounded monthly. Account B pays 4.45% compounded annually. A's APY is 4.49%; B's is 4.45%. On $25,000 over three years, A returns $3,523 and B returns $3,487, so the lower nominal rate wins by $36. Small, but it shows why the APY is the only number worth comparing.
Frequently Asked Questions (FAQs)
Which number should I compare between two offers?
APR for borrowing, APY for saving. Both bake in the thing the headline rate leaves out: fees for APR, compounding for APY. A lender or bank that will only quote a nominal rate is quoting the least informative number available.
Why is my credit card APR different from the interest I am charged?
Card APRs are nominal annual rates, but interest is usually compounded daily on the balance. A 22.9% APR compounds to an effective 25.7% over a year. Cards also apply different rates to purchases, cash advances and balance transfers, and payments are often allocated to the cheapest balance first.
What is a basis point?
One hundredth of a percentage point. A rate moving from 5.25% to 5.50% has risen by 25 basis points. The term exists to avoid the ambiguity in saying a rate rose by 0.25 percent, which could mean a quarter of a point or a quarter of a per cent of 5.25.
Can APR be lower than the interest rate?
Occasionally, when a lender credits you with rebates or the loan includes a subsidy. It is uncommon, and worth reading the terms carefully when it appears, since it usually means something has been netted off that may not apply to you.
How do I convert a monthly rate to an annual one?
Multiply by twelve for the nominal annual rate, or compound it for the effective one: (1 + monthly)^12 − 1. A 1.5% monthly rate is 18% nominal but 19.56% effective. Lenders quote the first; your balance follows the second.
Does a variable rate change the APR?
The quoted APR assumes the current rate holds for the whole term, which for a variable product is a presentation convention rather than a prediction. For adjustable-rate mortgages lenders usually publish a fully-indexed APR showing what applies if the rate resets to today's index plus margin.