How to Calculate a Loan Payment (Monthly Payment Formula)

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Издатель Jul 31, 2026

TITLE
How to Calculate a Loan Payment (Monthly Payment Formula)

DESCRIPTION
You borrow $20,000 for a car, the lender types in three numbers, and instantly says "$386.66 a month." What formula just ran? It's the loan payment formula — the one behind every car, student, and home loan — and it looks scarier than it is. In this Mini Lesson we read it slowly, then anatomize it: it has only three moving pieces. The monthly rate r/12 slices your yearly rate into twelve. The count 12t is how many payments you'll ever make. And the strange one — the negative exponent — runs compound growth backwards, shrinking each future payment to what it's worth today (that idea has a name, present value, but you don't need it to use the formula). Then we run it once — $20,000 at 6% for 5 years — plug in r/12 = 0.005 and 12t = 60, type the whole thing in as one calculator entry, and land on $386.66 a month. A quick sense-check shows 60 payments total $23,199.60, so the ~$3,200 gap is the interest. No lenders, no advice — just the math that prices every loan on earth.

You'll learn:
- What every symbol in the loan payment formula M = P(r/12) / (1 − (1 + r/12)^(−12t)) means
- Why the rate is divided by 12 and why the exponent is 12t
- What the negative exponent is actually doing (shrinking future payments to today's dollars)
- How to evaluate the formula in one calculator entry — $20,000 at 6% for 5 years → $386.66/mo
- Why the payments add up to more than you borrowed, and where the interest hides

[PLAYLIST LINK]

#math #learnmath #amortization #loanpayment

ORBITAL — Watch it click.