How do I find the interest rate on a loan I already paid?

Use the implied rate formula: r = (FV/PV)^(1/t) − 1, where PV is the original principal, FV is the total amount paid (sum of all payments), and t is the term in years. For example, paying $15,000 total on a $10,000 loan over 5 years gives r = (15000/10000)^(1/5) − 1 = 8.45% per year. Enter the values in the 'Find the Rate' tab above.

What is the difference between APR and APY?

APR (Annual Percentage Rate) is the stated nominal rate — it doesn't account for how often interest compounds within the year. APY (Annual Percentage Yield) is the effective rate that reflects compounding. For a 4.8% APR compounded monthly, APY = (1 + 0.048/12)^12 − 1 = 4.907%. For savings, you want the highest APY. For loans, watch the APR and compounding frequency. When compounding is annual, APR equals APY.

How do origination fees affect my actual interest rate?

Upfront fees reduce the net proceeds you receive while keeping your payments the same, effectively increasing your cost of borrowing. For example, a $300,000 mortgage at 5.5% APR with a $3,000 origination fee has an effective rate of approximately 5.62% — because you received only $297,000 in value but pay interest on $300,000. The shorter the loan term, the bigger the impact of fixed fees on the effective rate.

How do I convert APY to APR?

Use the formula: APR = n × [(1 + APY)^(1/n) − 1], where n is the number of compounding periods per year. For example, to find the monthly-compounding APR that produces a 5% APY: APR = 12 × [(1 + 0.05)^(1/12) − 1] = 12 × 0.004074 = 4.889%. You can do this conversion in the 'APR vs APY' tab by selecting 'APY → APR'.

Why does a credit card's APY differ so much from its APR?

Credit cards typically compound daily (365 times per year), which creates a bigger gap between APR and APY than monthly or quarterly compounding. At 24.99% APR with daily compounding, APY = (1 + 0.2499/365)^365 − 1 ≈ 28.38%. This means carrying a balance costs you 28.38% effectively per year, not just 24.99%. Always compare APYs when evaluating credit card costs.

Interest Rate Calculator

Q: Can I use this calculator for investments — not just loans?

Yes. The 'Find the Rate' tab works for any scenario where you know the starting value, ending value, and time period. Enter your initial investment as PV and the final portfolio value as FV to find the annualised return (CAGR). For example, if you invested $10,000 and it grew to $18,000 in 7 years, CAGR = (18000/10000)^(1/7) − 1 = 8.76% per year.

What interest rate are you actually paying or earning? Find the implied rate on any loan or investment, convert APR ↔ APY, and calculate the true effective rate including fees.

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Starting amount (PV)

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Final amount (FV)

Balance including all interest earned

Term (years)

Total duration in years

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Estimates only. Results are before tax. Consult a financial adviser for personalised guidance.

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How to Use This Calculator

Tab "Find the Rate" 🔍

Enter your starting amount (PV), ending amount or total payments (FV), and term in years. The calculator reverse-engineers the implied annual interest rate. Use the mode selector to distinguish between a savings scenario (you know the final balance) and a loan scenario (you know total payments made).

Tab "APR vs APY" 📊

Enter an APR to see the true APY at your chosen compounding frequency — or enter an APY to find the equivalent APR. Essential for comparing savings accounts, credit cards, and bonds that advertise different rate types. A visual bar chart shows the gap.

Tab "Effective Rate" ⚖️

Enter the nominal APR, loan amount, upfront fees, and discount points. The calculator uses IRR mathematics to find the effective APR — the true annual cost once fees are factored in. Useful for comparing mortgage offers with different rate/fee combinations.

The Formulas

1. Implied annual rate (reverse compound growth):
r = (FV / PV)^(1 / t) − 1
where PV = present value, FV = future value, t = years
This gives the CAGR (Compound Annual Growth Rate).

2. APY from APR (compounding n times per year):
APY = (1 + APR / n)^n − 1
where n = compounding periods per year (daily = 365, monthly = 12, etc.)

3. APR from APY:
APR = n × [(1 + APY)^(1/n) − 1]

4. Effective rate including fees (IRR approach):
Find r such that: Net proceeds = PMT × [1 − (1 + r_m)^(−n)] / r_m
where Net proceeds = Principal − upfront fees, PMT = monthly payment at nominal rate,
r_m = effective monthly rate, n = total months.
Solved via binary search (100 iterations). Effective APR = r_m × 12.

All calculations use standard financial mathematics. No country-specific regulations or tax adjustments are applied. Results are estimates and may differ from lender-quoted figures.

Worked Examples

Example 1 — Implied Rate: Paid $15,000 total on a $10,000 loan over 5 years

You borrowed $10,000 and made payments totalling $15,000 over 5 years. What annual interest rate were you paying?

Principal (PV)$10,000

Total payments (FV)$15,000

Term (t)5 years

Formular = (15,000 / 10,000)^(1/5) − 1

r = 1.5^0.2 − 1= 0.08447

Implied annual rate8.45% per year

The loan's implied rate was 8.45% per year. Note: this formula assumes annual compounding. The stated APR on an amortising loan with monthly payments would be slightly different, but this gives a quick reverse-engineering answer from total amounts.

Example 2 — APR vs APY: Credit card at "24.99% APR" (daily compounding)

Your credit card charges 24.99% APR. The fine print says interest compounds daily. What do you actually pay per year?

APR (stated)24.99%

CompoundingDaily (n = 365)

FormulaAPY = (1 + 0.2499/365)^365 − 1

Daily rate0.2499 / 365 = 0.000685

APY = (1.000685)^365 − 1= 0.2838

Effective APY28.07% per year

The true annual cost is 28.07% APY — over 3 percentage points higher than the advertised 24.99%. On a $5,000 balance, that difference is an extra $154 in interest per year. Daily compounding is the norm for credit cards, making the APY gap particularly large at high rates.

Example 3 — Effective Rate: Mortgage at 5.5% APR + $3,000 origination fee on $300,000

A lender offers a 30-year mortgage at 5.5% APR with a $3,000 origination fee. What is the true effective rate?

Loan amount$300,000

Nominal APR5.5%

Origination fee$3,000

Net proceeds$300,000 − $3,000 = $297,000

Monthly payment$1,703.37 (at 5.5%)

Effective APR5.62% per year

The effective rate is 5.62% — 12 basis points above the stated 5.5%. While this seems small, it represents an additional ~$6,900 in total borrowing cost over the life of the loan. If the same lender offered 5.6% with no fees, the no-fee option would be slightly cheaper. Use the Effective Rate tab to compare offers objectively.

Understanding Interest Rates: Key Concepts

APR vs APY — Why They Both Matter

APR (Annual Percentage Rate) is the headline number — the rate before compounding. Banks use APR to make loan rates look lower and savings rates look higher in marketing materials. APY (Annual Percentage Yield) is the effective rate after compounding is applied within the year. For savings, always compare APY. For loans, compare APR but check the compounding frequency — more frequent compounding means higher true cost.

The Compounding Gap

The gap between APR and APY grows with rate level and compounding frequency. At 1% APR, daily vs annual compounding makes almost no difference. At 25% APR (credit cards), daily compounding adds 3+ percentage points to the effective rate. The formula APY = (1 + APR/n)^n − 1 captures this exactly.

Fees Change Everything

Upfront fees effectively increase your borrowing cost because you receive less money than you borrowed, yet pay interest on the full amount. A $1,000 fee on a $10,000 loan is far more costly than the same $1,000 fee on a $500,000 mortgage — proportionally. Short-term loans amplify this effect: a $3,000 fee on a 5-year loan increases the effective rate more than the same fee on a 30-year loan.

CAGR — The Investment Equivalent

The Compound Annual Growth Rate (CAGR) is the same maths as the implied interest rate: r = (FV/PV)^(1/t) − 1. If a portfolio grew from $50,000 to $90,000 over 6 years, CAGR = (90,000/50,000)^(1/6) − 1 = 10.27%. This is the single annual rate that would produce the same outcome as the actual year-by-year performance — useful for comparing investments over different time horizons.

Discount Points

When taking a mortgage, lenders may offer a lower rate in exchange for "points" paid upfront. One point = 1% of the loan amount. Whether buying points is worthwhile depends on how long you hold the loan — the Effective Rate tab factors points into the true borrowing cost so you can compare deals accurately.

Frequently Asked Questions

How do I find the interest rate on a loan I've already paid?▼

Use the "Find the Rate" tab. Enter the original loan amount as PV, the total of all payments you made as FV, and the loan term in years. The calculator applies r = (FV/PV)^(1/t) − 1 to give the implied annual rate. For example: borrowed $10,000, paid back $15,000 total over 5 years = 8.45% implied annual rate.

My savings account says 4.8% APR but the APY is 4.91% — which is real?▼

APY is the real effective return. With monthly compounding at 4.8% APR, APY = (1 + 0.048/12)^12 − 1 = 4.907%. The 4.91% is what you actually earn over a full year. When comparing savings accounts, always compare APY — not APR — because it accounts for compounding frequency differences between accounts.

Does this calculator account for taxes on interest?▼

No — this is a universal pre-tax calculator. Interest earned on savings is generally taxable income in most countries, and the rate varies by jurisdiction and account type. The effective rate shown is a gross figure before any withholding or income tax. Use the "Calculate for your country" links below for tax-specific calculators.

Why does the effective rate change so little for a 30-year mortgage but a lot for a short loan?▼

Upfront fees are spread over the life of the loan. A $3,000 fee on a 30-year mortgage amortises to about $8.33 per month — a tiny fraction of each payment. The same $3,000 fee on a 2-year loan amortises to $125 per month, a much larger proportion. That's why short-term loans and early payoffs amplify the effective rate impact of fixed fees significantly.

Can I use the implied rate tool for investments?▼

Yes. Enter your initial investment as PV and the final portfolio value as FV to find your CAGR (Compound Annual Growth Rate). For example: $10,000 grew to $18,000 in 7 years → CAGR = (18,000/10,000)^(1/7) − 1 = 8.76% per year. This is the annualised return regardless of how each year performed individually.

What is the Rule of 72 and how does it relate to interest rates?▼

The Rule of 72 is a shortcut: divide 72 by the annual rate to estimate how many years it takes to double your money. At 8%, money doubles in 9 years. At 6%, in 12 years. To verify, use the "Find the Rate" tab with FV = 2 × PV over the estimated years — the implied rate should match your input rate. Useful for quickly gauging compound growth without a calculator.

How does a daily-compounding credit card differ from a monthly-compounding loan?▼

At the same APR, daily compounding produces a higher APY (effective rate) than monthly compounding. At 20% APR: daily compounding gives APY = 22.13%; monthly gives 21.94%. The difference is small at moderate rates but grows at high rates like credit cards (20–30%+). For loans, more frequent compounding means you pay more over the year for the same stated APR. Always check the compounding frequency, not just the headline rate.

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