Calculator
Finance
MathLoan Calculator
Calculate loan payments, total interest and a full amortization schedule with extra payments and APR/APY. Export the dated schedule to CSV.
Amortized Loan: Paying Back a Fixed Amount Periodically
Use this calculator for basic calculations of common loan types such as mortgages, auto loans, student loans, or personal loans, or click the links for more detail on each.
Deferred Payment Loan: Paying Back a Lump Sum Due at Maturity
Use this calculator to determine the future value of a loan where no payments are made until maturity. Interest compounds over the loan term.
Bond: Paying Back a Predetermined Amount Due at Loan Maturity
Use this calculator to compute the initial value of a bond/loan based on a predetermined face value to be paid back at bond/loan maturity.
Have feedback? Report bugs, suggest features, or share your thoughts — we read them allWhat is a Loan Calculator?
A loan calculator is a versatile financial tool designed to help you understand the true cost of borrowing money. Whether you're considering a mortgage, auto loan, student loan, or personal loan, this calculator provides detailed insights into your payment obligations, total interest costs, and repayment schedules.
This comprehensive loan calculator includes three different calculation methods to cover various loan types: Amortized Loans (regular periodic payments), Deferred Payment Loans (lump sum at maturity), and Bonds (present value calculations). Each type serves different financial needs and understanding them helps you make informed borrowing decisions.
Amortized Loan: Fixed Periodic Payments
An amortized loan is the most common type of loan where you make regular, equal payments over the loan term. Each payment includes both principal and interest, with the proportion shifting over time. Early payments are mostly interest, while later payments are mostly principal.
The formula for calculating the periodic payment amount is:
PMT = P × [r(1+r)n] / [(1+r)n - 1]
Where:
- PMT = Payment amount per period
- P = Principal loan amount (initial amount borrowed)
- r = Interest rate per payment period
- n = Total number of payments
Deferred Payment Loan: Lump Sum at Maturity
A deferred payment loan is a type of loan where no payments are made during the loan term. Instead, interest accrues and compounds, and the entire amount (principal plus accumulated interest) is paid at maturity. This is common in certain investment vehicles, student loans during school years, or specialized financial products.
The formula for calculating the amount due at maturity is:
A = P(1 + r/n)nt
Where:
- A = Amount due at maturity (future value)
- P = Principal loan amount (initial amount borrowed)
- r = Annual interest rate (as decimal)
- n = Number of times interest compounds per year
- t = Time in years
Bond: Present Value of Future Amount
A bond calculation determines how much you would receive today (present value) for a loan that requires you to pay back a specific amount in the future. This is essentially the reverse of the deferred payment loan - instead of knowing what you borrow and calculating what you'll owe, you know what you'll owe and calculate what you can borrow today.
The formula for calculating the present value (amount received at start) is:
P = F / (1 + r/n)nt
Where:
- P = Present value (amount received when loan starts)
- F = Future value (predetermined amount due at maturity)
- r = Annual interest rate (as decimal)
- n = Number of times interest compounds per year
- t = Time in years
Practical Examples
Example: Amortized Loan
A $100,000 loan at 6% annual interest for 10 years with monthly payments:
- Loan Amount: $100,000
- Interest Rate: 6% per year (compounded monthly)
- Loan Term: 10 years (120 months)
- Payment Frequency: Monthly
- Monthly Payment: $1,110.21
- Total Payments: $133,224.60
- Total Interest: $33,224.60
- Principal: 75% | Interest: 25%
Example: Deferred Payment Loan
A $100,000 loan at 6% annual interest for 10 years with no payments (compounded annually):
- Loan Amount: $100,000
- Interest Rate: 6% per year (compounded annually)
- Loan Term: 10 years
- Payment Frequency: None (deferred)
- Amount Due at Maturity: $179,084.77
- Total Interest: $79,084.77
- Principal: 56% | Interest: 44%
Example: Bond Calculation
A bond requiring $100,000 payment in 10 years at 6% annual interest (compounded annually):
- Amount Due at Maturity: $100,000
- Interest Rate: 6% per year (compounded annually)
- Loan Term: 10 years
- Amount Received Today: $55,839.48
- Total Interest Paid: $44,160.52
- Principal: 56% | Interest: 44%
Common Loan Types and Applications
- Mortgages: Home loans typically use amortized payment structures with 15-30 year terms. Fixed-rate mortgages have constant payments, while adjustable-rate mortgages (ARMs) can change.
- Auto Loans: Vehicle financing usually follows amortized schedules with 3-7 year terms. New cars often qualify for better rates than used vehicles.
- Student Loans: Education loans may be deferred during school (interest accrues) then switch to amortized payments after graduation. Federal and private loans have different terms.
- Personal Loans: Unsecured loans for various purposes, typically amortized over 2-7 years. Interest rates vary based on creditworthiness.
- Business Loans: Commercial financing can use any structure - amortized for equipment purchases, deferred for startups, or balloon payments for real estate.
- Bonds and Securities: Corporate and government bonds pay a fixed amount at maturity, with the purchase price reflecting present value calculations.
- Payday and Short-term Loans: High-interest loans with lump sum repayment, often due in 2-4 weeks. Generally expensive and risky.
- Interest-Only Loans: Pay only interest during initial period, then either balloon payment or convert to amortized schedule.
Tips for Managing Loans
- Compare APR vs APY: APR (Annual Percentage Rate) shows simple interest, while APY (Annual Percentage Yield) includes compounding effects. Higher compounding frequency means higher effective rate.
- Extra Payments: Additional principal payments on amortized loans reduce total interest significantly. Even small extra payments early in the loan term make a big difference.
- Shorter Terms Save Money: Loans with shorter terms have higher monthly payments but much lower total interest. A 15-year mortgage costs far less than 30-year, even at similar rates.
- Shop Around for Rates: Interest rates vary significantly between lenders. A difference of 0.5% can mean thousands in savings over the loan term.
- Consider Total Cost: Don't focus only on monthly payment - calculate total interest paid over the life of the loan. Lower payments often mean more interest.
- Understand Compound Frequency: Monthly compounding is more expensive than annual compounding at the same stated rate. Know how your loan compounds.
- Deferred Interest Risks: Loans with deferred payment can balloon to unexpected amounts. Interest compounds on interest, growing the balance exponentially.
- Credit Score Matters: Better credit scores qualify for lower interest rates, saving substantial money. Work on improving credit before applying for major loans.
- Read the Fine Print: Watch for prepayment penalties, variable rates, balloon payments, and other terms that could cost extra or create payment surprises.
- Emergency Fund First: Before taking on new debt, ensure you have 3-6 months of expenses saved. This prevents defaulting if financial situations change.
When to Use Each Loan Type
- Use Amortized Loans When: You want predictable monthly payments, are financing a home or vehicle, need to build equity gradually, or prefer consistent budgeting with no surprises at maturity.
- Use Deferred Payment Loans When: You expect higher future income (like students), need to minimize current cash flow obligations, have investments earning more than loan interest, or are handling short-term cash flow issues.
- Use Bond/Present Value When: You're pricing investment securities, comparing loan offers, determining fair value of future obligations, or structuring business deals with future payments.
- Avoid Deferred Loans When: Interest rates are high (compounding costs explode), you're uncertain about future income, the loan term is very long, or you have trouble managing growing obligations.
- Refinancing Considerations: Refinance amortized loans when rates drop 1%+, you can shorten term without payment stress, you can eliminate PMI, or you need to convert variable to fixed rates.
Frequently Asked Questions
The amortization formula is PMT = P × [r(1+r)^n] / [(1+r)^n − 1], where P is principal, r is the periodic rate, and n is the total number of payments. The reason simple division (loan ÷ months) understates the payment is that you're paying interest on the outstanding balance each month, not the average balance. On a $300,000 30-year mortgage at 7%, simple division gives $833/month, but the true amortized payment is $1,996/month because the balance shrinks slowly — after 10 years you've still got 86% of the principal outstanding. The CFPB's TILA-RESPA Loan Estimate (mandatory since 2015) shows you exactly this number alongside the total finance charge over the loan life.
APR (Annual Percentage Rate) is the stated yearly rate before compounding effects. APY (Annual Percentage Yield) reflects the actual effective rate after compounding within the year. For a loan quoted at 6% APR compounded monthly, the APY is (1 + 0.06/12)^12 − 1 = 6.17%. Federal law (TILA, Regulation Z) requires lenders to disclose APR which includes most upfront fees (origination, discount points, mortgage insurance) amortized over the loan term — making it the legally standardized number for comparing offers. The Loan Estimate from any U.S. mortgage lender includes APR specifically so you can compare apples-to-apples; the FDIC found in a 2024 supervisory letter that the most common consumer mistake is comparing one lender's note rate to another's APR.
With a deferred loan, interest accrues and compounds on a growing balance instead of being paid down each period. The formula A = P(1 + r/n)^(nt) means that at 6% compounded monthly, $30,000 left to compound for 4 years of college becomes $38,113 by graduation — and that's the new principal you'll amortize. The U.S. Department of Education's Federal Student Aid data shows roughly $1.77 trillion in outstanding federal student debt as of 2025, with unsubsidized Direct Loans accruing interest in-school being a major driver of post-graduation balance shock. If you can make interest-only payments during deferment (about $150/month on that same $30k), you avoid all of that compounded growth.
A zero-coupon bond calculation uses P = F / (1 + r/n)^(nt) — the present value of a future lump sum, discounted at the prevailing rate. A $10,000 face-value, 10-year Treasury STRIP at 4.5% would sell today for about $6,415. Borrowers encounter this in three real situations: (1) seller-financed property deals where you owe one balloon at closing — present value tells you the fair purchase discount; (2) corporate or municipal zero-coupon bond issues where the issuer receives less than face today; (3) structured settlements where you trade a future stream for cash now. The IRS imputes interest on below-market loans using AFR rates published monthly precisely because the difference between face and present value IS interest, even when no coupons are paid.
It saves real money but for a specific mechanical reason: 26 biweekly half-payments equal 13 monthly payments per year, not 12 — you're sneaking in one extra full payment annually. On a 30-year $300,000 loan at 7%, switching from monthly to true biweekly saves about $93,000 in interest and pays the loan off roughly 6 years early. The catch: many servicers hold the half-payments and only apply them monthly, neutralizing the benefit, while still charging $5–$10 setup fees. The Consumer Financial Protection Bureau warned about this in a 2022 supervisory bulletin. The free alternative is making one extra principal-only payment per year yourself, which produces almost identical results without the fee.
The classic rule of thumb is to refinance when you can drop your rate by 1 percentage point or more, but the right calculation is breakeven months = total closing costs ÷ monthly savings. If refinancing costs $5,000 and saves $200/month, breakeven is 25 months — refinance only if you'll stay in the home longer than that. Freddie Mac's 2024 Refinance Report found the average closing cost is 2–5% of loan amount. Also factor in resetting the amortization clock: refinancing a 22-year-remaining loan back into a new 30-year stretches your interest payment window even at a lower rate, so check the total-interest-over-life figure, not just monthly payment. Many borrowers refinance into 15- or 20-year terms specifically to avoid this trap.
Compounding frequency determines how often unpaid interest gets added to principal so it itself can earn interest. At a 7% nominal APR, the effective annual rate climbs from 7.000% (annual) → 7.123% (semi-annual) → 7.186% (quarterly) → 7.229% (monthly) → 7.247% (daily) → 7.251% (continuous). The differences look small but on a $500,000 mortgage over 30 years, daily vs monthly compounding adds roughly $14,000 to total interest. Most U.S. mortgages compound monthly, but credit cards compound daily — which is why a 20% credit card APR has an effective rate closer to 22.1%. Federal Reserve consumer-credit data (G.19 series) tracks both nominal and effective rates separately.
An amortization schedule lists every payment with its split into interest (computed on the prior balance) and principal (the rest), plus the running balance and cumulative interest. To audit it, check three things: (1) each row's interest equals previous balance × periodic rate; (2) payment minus interest equals the principal applied; (3) the final balance lands at zero. The crossover point is the payment where principal first exceeds interest — on a 30-year loan at 7% that doesn't happen until around payment 220 of 360, which is why early payoff saves so much. Use this tool's 'Loan start date' field to attach real calendar dates, then 'Download CSV' to export the full dated schedule (Payment #, Date, Payment, Principal, Interest, Cumulative interest, Balance) for archiving, underwriting review, or import into Excel. The extra-payment field lets you model paying off the loan early and see exactly how many payments and how much interest you save.
The note rate (or coupon rate) is the raw interest rate used to compute your payment. APR is broader: under TILA/Regulation Z it amortizes most upfront finance charges — origination fees, discount points, lender-paid mortgage insurance, certain closing costs — over the loan term and expresses the result as an annualized rate. So a 6.50% note rate with 2 discount points and $3,000 in fees might carry a 6.85% APR. APR is the legally standardized figure for comparing offers, but it has a blind spot: it assumes you hold the loan to term, so paying points (which raises closing cost but lowers the note rate) only beats a no-points loan if you keep the loan past the breakeven horizon. For true cost when you expect to sell or refinance early, compare total dollars paid over your actual holding period — note rate payments plus the amortized fees you won't recover — rather than the to-maturity APR alone. The CFPB Loan Estimate shows both the APR and a 5-year 'total you will have paid' figure precisely for this reason.
A home equity loan or HELOC at 8% can replace credit card debt at 22%, cutting interest costs by more than half on the same balance. The mathematical case is compelling — on $40,000 of card debt, switching to a 10-year secured loan saves roughly $30,000 in interest while cutting the payoff timeline from 30+ years (making minimums) to 10. But the structural risk is severe: you've converted unsecured debt into debt collateralized by your house, meaning a job loss can now mean foreclosure rather than just credit damage. The FTC's 2023 consumer alert specifically warns against repeatedly tapping equity for consumption, since 30%+ of equity-loan consolidators end up running cards back up within 5 years per a 2024 NY Fed Liberty Street Economics study. Use only with a written debt-elimination plan and frozen card accounts.
FINANCIAL CALCULATORS22
WUTOOLS