Boat Loan Calculator

Inputs

$
$
%
years

Results

Monthly Payment

$427.33

≈ 8 tanks of gas

Total Cost

$60,279.16

≈ 5 years of state college

Total Interest$15,279.16
Loan Amount$36,000.00
Loan-to-Value80%
Down Payment20%
Total Payments$51,279.16

Amortising loan payment

  1. 1.Convert the annual rate to a monthly rate
    i=7.5%12=0.00625

    Payments are monthly, so every term in the formula has to be expressed per month.

  2. 2.Count the payments
    n=10×12=120

    The number of monthly payments over the whole term.

  3. 3.Solve for the level payment
    M=36,000×0.00625×2.1120652.1120651=427.33

    This comes from setting the present value of all n equal payments equal to the amount borrowed, then solving for the payment. The (1+i)ⁿ − 1 in the denominator is the sum of a geometric series — the same series that drains a pension or decays a drug in plasma, which is why one formula family serves calculators across several hubs.

Simon Stevin published the first printed interest tables, including the present value of an annuity — the relationship this payment formula inverts. Until then such tables were guarded as trade secrets by lenders.
Simon Stevin, Tafelen van Interest, Antwerp·1582