How To Calculate Interest on Your Loan: A Step-By-Step Guide To Simple and Amortized Interest

Most personal loans, auto loans and mortgages use daily simple interest with monthly amortization, meaning interest accrues on your remaining balance each day and your monthly payment covers that period's interest first, with the rest reducing your principal.

A separate, simpler method called basic simple interest (I = P × r × t) applies to some short-term loans without monthly payments.

Here's how to calculate both, plus how compound interest works if you're comparing a loan against a savings or investment return.

Key Takeaways

• Most installment loans use daily simple interest with amortization, not a single lump-sum calculation, so your payment splits between interest and principal every month.

• The basic simple interest formula (I = P × r × t) works for loans without monthly payments, like some short-term notes, where interest accrues once on the full principal for the entire term.

• Total interest doesn't scale linearly with your rate. On a $10,000, 36-month loan, going from 6% to 12% APR roughly doubles your total interest, but going from 12% to 24% more than doubles it again, since the amortization math compounds.

• Compound interest, used for savings rather than typical loan interest, grows faster than simple interest because it earns returns on previously earned interest, not just the original principal.

• Your APR, not just your interest rate, tells the true cost of a loan, since APR folds in fees like an origination charge that a bare interest rate doesn't reflect.

Summary generated by AI, verified by MoneyLion editors

Method 1: Basic Simple Interest

This is the formula most people learn first, and it works well for a loan where interest accrues once on the full principal, with no monthly payments reducing the balance along the way.

The formula:

Interest = Principal × Rate × Time

Where:

• Principal (P) is the amount borrowed.

• Rate (r) is the annual interest rate, expressed as a decimal (6% = 0.06).

• Time (t) is the loan term in years.

Worked example: You borrow $10,000 at a 6% annual rate for three years, with no monthly payments and the full balance due at the end.

• Interest = $10,000 × 0.06 × 3 = $1,800

• Total repayment = $10,000 + $1,800 = $11,800

This method assumes the full principal accrues interest for the entire term, since nothing is paid down along the way. It's common for certain short-term notes, but it's not how most personal loans, auto loans or mortgages work.

Method 2: Daily Simple Interest With Amortization

This is what most loans use. Most installment loans, personal loans, auto loans and mortgages included, use a method sometimes called "simple interest" by lenders, but it works differently than the basic formula above. Interest accrues daily on your current outstanding balance, and each monthly payment is split between that period's interest charge and reducing your principal. As your principal shrinks, the interest portion of each payment shrinks too, and more of your payment goes toward principal over time.

The monthly payment formula:

M = P × [r(1+r)ⁿ] / [(1+r)ⁿ − 1]

Where:

• M is your monthly payment.

• P is the principal (loan amount).

• r is your monthly interest rate (annual rate ÷ 12).

• n is the total number of monthly payments.

Worked example: You borrow $10,000 at 12% APR over 36 months.

• Monthly rate: 0.12 ÷ 12 = 0.01

• Plug into the formula: M = $10,000 × [0.01(1.01)³⁶] / [(1.01)³⁶ − 1] ≈ $332.14

• Total paid over 36 months: $332.14 × 36 = $11,957.04

• Total interest paid: $11,957.04 − $10,000 = $1,957.04

How Total Interest Changes by APR

Here's how total interest scales on that same $10,000, 36-month loan at a few different rates.

Going from 6% to 12% roughly doubles the total interest, but going from 12% to 24% more than doubles it again, since a higher rate both raises the monthly payment and slows how quickly the balance shrinks.

Notice this daily-amortized result is meaningfully different from the basic simple interest method above, which would have produced $1,800 in interest on a 6% rate over three years on a $10,000 loan. That's because this method reduces the balance every month as you pay it down, so less interest accrues over the loan's remaining life compared to a lump-sum calculation that leaves the full principal outstanding the entire time.

MoneyLion's guide on whether you can pay off a personal loan early walks through how that math works in practice.

MoneyLion offers a service to help you find personal loan offers. Based on the information you provide, you can get matched with offers for up to $100,000 from our top providers. You can compare rates, terms and fees from different lenders and choose the best offer for you.

Method 3: Compound Interest

Compound interest isn't typically how loan interest works. It's more commonly relevant to savings accounts, CDs and investments, but it's worth understanding for comparison, especially if you're weighing whether to pay down a loan or grow savings instead.

The formula: A = P(1 + r/n)^(nt)

Where:

• A is the final amount after interest.

• P is the principal.

• r is the annual rate, as a decimal.

• n is the number of times interest compounds per year (12 for monthly, 365 for daily).

• t is the time in years.

Worked example: You deposit $10,000 in a savings account at 4% APY, compounded monthly, for three years.

• A = $10,000 × (1 + 0.04/12)^(12×3)

• A = $10,000 × (1.003333)³⁶

• A ≈ $11,270.32

• Total interest earned: $11,270.32 − $10,000 = $1,270.32

Compound interest grows faster than simple interest over time because you earn returns on your previously earned interest, not just your original principal, the reverse side of why compound interest can work against you on credit card debt that isn't paid off in full each month.

If you're weighing whether extra cash is better spent paying down a loan or growing savings, comparing your loan's APR against a high-yield savings account rate is a useful place to start.

Why Does APR Matter More Than the Interest Rate Alone?

The interest rate calculations above only capture part of a loan's true cost. Your annual percentage rate (APR) rolls in the interest rate plus certain fees, like a loan origination fee, giving you a single number that better reflects the total cost of borrowing. Two loans with the same interest rate but different origination fees will have different APRs, and comparing APRs, not just interest rates, is the more accurate way to shop between lenders.

How Do You Check Your Own Loan's Numbers?

1. Find your loan's interest rate and APR on your loan agreement or Truth in Lending disclosure. They'll rarely be identical if any fees apply.

2. Confirm your compounding or accrual method. Most installment loans use daily simple interest with monthly amortization, described in Method 2 above.

3. Recalculate your payment using the formula above to double-check your lender's disclosed figure matches what you'd expect.

4. Compare total interest across term lengths. A longer term lowers your monthly payment but increases your total interest paid, since more months means more time for interest to accrue on a slower-shrinking balance.

Bottom Line

How you calculate interest on a loan depends entirely on which method your lender uses.

Most installment loans, personal loans, auto loans and mortgages, use daily simple interest with monthly amortization, where your balance shrinks with each payment and less interest accrues over time. A simpler lump-sum formula (I = P × r × t) applies to certain short-term loans without monthly payments, and compound interest, while not typical for loan structuring itself, is worth understanding for comparison against savings and investment growth.

Whichever method applies to you, comparing APR rather than just the bare interest rate remains the clearest way to judge a loan's true total cost.

Key Terms

• Principal: The original amount borrowed, before any interest is added.

• Simple interest: Interest calculated only on the original principal (or, in daily simple interest, on the current outstanding balance), rather than on previously accrued interest.

• Compound interest: Interest calculated on both the principal and any previously earned interest, causing balances to grow faster over time.

• Amortization: The process of paying down a loan through scheduled payments that cover interest first, then reduce principal, with the interest portion shrinking as the balance does.

• Annual percentage rate (APR): A standardized measure of a loan's yearly cost that includes the interest rate plus certain fees, such as an origination fee.

• Interest rate: The base percentage cost of borrowing, before factoring in fees. Distinct from APR, which includes those fees.

Summary generated by AI, verified by MoneyLion editors

Sources

• What Is the Difference Between a Loan Interest Rate and the APR?, Consumer Financial Protection Bureau

• What Is Amortization?, Consumer Financial Protection Bureau

Summary generated by AI, verified by MoneyLion editors

FAQ

Here are quick answers to common questions about calculating interest on a loan:

How do you calculate simple interest on a loan?

Multiply the principal by the annual interest rate (as a decimal) by the time in years: Interest = P × r × t. For example, $10,000 at 6% for three years equals $1,800 in interest, for a total repayment of $11,800.

How is interest calculated on a personal loan?

Most personal loans use daily simple interest with monthly amortization: interest accrues daily on your outstanding balance, and each payment covers that period's interest first, with the remainder reducing your principal. This differs from a basic lump-sum simple interest calculation.

What's the difference between simple interest and compound interest?

Simple interest is calculated only on the principal or current balance. Compound interest is calculated on the principal plus any previously earned interest, which makes it grow faster over time. Most loans use a simple-interest-based method, while savings accounts and investments typically use compound interest.

Why does my loan's APR differ from its interest rate?

APR includes the interest rate plus certain fees, like an origination fee, giving you a more complete picture of the loan's total cost. Two loans with identical interest rates can have different APRs if their fees differ.

Does a longer loan term mean more total interest?

Generally, yes. A longer term lowers your monthly payment, but it also gives interest more time to accrue on a balance that's paying down more slowly, which usually increases the total interest you pay over the life of the loan.