Loan calculator

The formula, step by step

A fixed-rate loan paid monthly has one payment that never changes, found with this formula:

M = P × r × (1 + r)^n ÷ ((1 + r)^n − 1)

P is the amount borrowed, r is the monthly rate (the yearly rate ÷ 12 ÷ 100) and n is the number of monthly payments (years × 12).

Worked example: $25,000 at 6% for 5 years.

• r = 6 ÷ 12 ÷ 100 = 0.005, and n = 5 × 12 = 60
• (1.005)^60 = 1.34885
• M = 25,000 × 0.005 × 1.34885 ÷ 0.34885 = $483.32
• Total paid = 483.32 × 60 = $28,999.20, so the total interest is $3,999.20

At 0% the formula would divide by zero, so Octoolo simply splits the amount evenly: $12,000 over 4 years is $250 a month. You can check any result by typing the formula into the calculator: 25000 × 0.005 × 1.005^60 ÷ (1.005^60 − 1).

Where each payment goes

Every payment covers that month's interest first, and the rest pays down the balance. In the example above, month one's interest is 25,000 × 0.005 = $125, so $358.32 of the $483.32 goes to the balance, which drops to $24,641.68. Month two's interest is $123.21 and $360.11 goes to the balance. The interest part shrinks every month and the balance part grows.

On a long loan the early payments are mostly interest. A $300,000 mortgage at 6.5% over 30 years costs $1,896.20 a month; in the first month $1,625.00 of that is interest and only $271.20 reduces what you owe.

Octoolo's loan calculator shows the payment and the totals, not this month-by-month breakdown: it has no amortization table and no field for extra payments. The two steps above are the whole method if you want to work out a few months by hand: interest is the balance times r, and the rest of the payment comes off the balance.

How the term and rate change the cost

Borrowing $30,000 at 7%:

A longer term lowers the payment but raises the total: going from 4 to 6 years cuts the payment by about $207 a month and adds $2,343.26 of interest. Comparing terms side by side is also the closest this calculator gets to modeling extra payments, since paying more each month amounts to a shorter loan. The rate counts as much: the same $30,000 over 5 years costs $566.14 a month and $3,968.22 of interest at 5%, but $622.75 and $7,365.04 at 9%.

For a mortgage the stakes are bigger. $300,000 at 6.5% costs $2,613.32 a month over 15 years with $170,397.98 of interest, or $1,896.20 a month over 30 years with $382,633.47 of interest, more than the loan itself.

What the payment leaves out

• Fees and APR. Lenders quote an interest rate and an APR, which adds fees spread over the term. Enter the interest rate to get the payment; use the APR to compare lenders.
• Taxes and insurance. A mortgage payment often includes property tax, home insurance and mortgage insurance on top of principal and interest. This calculator covers only principal and interest.
• Variable rates. If the rate can change, the result holds only until it does.
• Other compounding. The math assumes monthly payments with interest worked out monthly, as is usual for US car loans, personal loans and mortgages. Canadian fixed-rate mortgages compound twice a year, so their payment comes out slightly different.
• Balloon payments, payment holidays and extra payments are not modeled.

It is a calculator, not financial advice: your lender's documents are the final word on what you owe.