Loans & Mortgages

A mortgage, car loan or student loan. What will you pay, how much can you borrow, what is the rate, or how long until it is paid off? See the whole repayment schedule, how much of it is interest, and how much sooner it is paid off if you pay a little extra.

FinanceLoansMortgageAmortization

Inputs

Input examples

An annuity loan has the same payment every period: first mostly interest, later mostly repayment. A linear loan repays the same part of the loan every period plus the interest on what is left, so the payments start high and go down. Click Solve next to the quantity you want to find. The rate is the yearly (nominal) rate, charged every payment period. The extra payments are optional. For education only — not financial advice; real loans can have fees.

Currency

Loan amount L — €

Interest rate r — % per year

Term t — years

Payment per month M — €

Pay off early — optional

Extra every month — €

One-off extra payment — €

Paid after — years

How a Loan is Repaid

Every payment consists of two parts: interest on the debt that is still open, and repayment that makes the debt smaller. Most mortgages and personal loans are annuity loans: the payment stays the same, so the repayment part grows as the interest part shrinks. With a linear loan you repay faster at the start: the first payments are higher, but the debt falls sooner and you pay less interest in total.

Over a long term the interest adds up: a 30-year mortgage at 4% costs almost three-quarters of the loan amount again in interest. Paying extra goes straight off the debt, so from then on you no longer pay interest on it, for all the remaining years. Extra payments early in the loan save the most; the interest you save is in effect a return equal to the loan’s rate.

300k, 4%, 30 y1 432 a month

total interest≈ 216k (linear: 181k)

+200 a month≈ 6 years sooner

checkearly-repayment fees

What You Still Owe

balance

remaining debt

interest paid so far

debt without the extra payments

Result

Enter the values above

Interest and Repayment per Year

per year

repayment

interest

Repayment Schedule

totals per year

Year	Paid	Interest	Repayment	Still owed

Monthly Payment per 100 000

annuity loan

Rate	10 years	20 years	30 years
2%	920.13	505.88	369.62
4%	1 012.45	605.98	477.42
6%	1 110.21	716.43	599.55
8%	1 213.28	836.44	733.76

Worked Techniques

The Annuity Payment

The loan equals the present value of all future payments. Use the rate per period (yearly rate / 12 for monthly payments) and the number of payments. Turned around, the payment you can afford sets the loan.

Example: 20 000 at 6.5% over 5 years: 391.32 a month; 1 500 a month at 4.5% for 25 years borrows 269 865.

One Row of the Schedule

Take the debt at the start of the period, multiply by the rate per period; what is left of the payment reduces the debt. A linear loan repays L/N every period, so its total interest is i L (N+1)/2.

Example: 300 000 at 4%: first month 1 000 interest, 432.25 repayment; linear: 180 500 interest in total.

Paying Extra

With an extra X every period you effectively pay M + X, so the loan ends sooner. A one-off payment simply makes the balance smaller from then on.

Example: 300 000, 4%: 1 432.25 + 200 → 285 months instead of 360, saving 50 412 of interest.

Sources & Verification

References

R. A. Brealey, S. C. Myers & F. Allen, Principles of Corporate Finance, 13th ed., McGraw-Hill Education, 2020 — Ch. 2 (How to Calculate Present Values: annuities and loan repayment).