Borrow $25,000 at 5% a year for 5 years, paid monthly.
Monthly rate r = 5% ÷ 12 = 0.4167%; payments n = 5 × 12 = 60.
Payment = 25,000 × r ÷ (1 − (1 + r)^−60).
Over 60 payments you pay $28,306.88 in total.
Payment: $471.78 a month. Total interest: $3,306.88.
A 30-year mortgage
A $400,000 home with 20% down, 6.5% for 30 years, property tax 1.1% a year and insurance $1,500 a year.
Loan = 400,000 − 80,000 = $320,000.
Principal and interest at 6.5% over 360 payments = $2,022.62.
Tax 4,400 ÷ 12 = $366.67 and insurance 1,500 ÷ 12 = $125.00 a month.
Monthly payment: $2,514.29. Interest over the loan: $408,140.64.
Paying a little extra
A $200,000 loan at 6% for 30 years ($1,199.10 a month), with $100 extra each month.
The extra goes straight to the principal, so less interest builds up.
The loan is paid off after 295 payments instead of 360.
You finish 5 years 5 months sooner and save $49,138.85 in interest.
贷款还款公式
payment = P × r ÷ (1 − (1 + r)^−n)r = yearly rate ÷ payments per year, n = years × payments per year
P is the amount borrowed. Each payment first covers the interest on what you still owe (balance × r); the rest pays down the principal. That is why early payments are mostly interest and later ones mostly principal.