How loan comparison math works
Every loan quote boils down to the amortization formula: M = P × r(1+r)n ÷ ((1+r)n − 1), where P is the amount borrowed, r the monthly interest rate (annual rate ÷ 12), n the number of monthly payments, and M the fixed monthly payment. Each payment covers that month's interest first; the rest chips away the principal. Two numbers decide which offer is cheaper: the total paid (M × n) and the total interest (total paid − P). The advertised rate alone can mislead — APR (annual percentage rate) folds fees and charges into one comparable figure, which is why it is usually slightly higher than the nominal rate.
Worked example: $20,000 at 7% for 5 years
P = 20,000, annual rate 7%, so r = 0.07 ÷ 12 = 0.005833, n = 60. (1.005833)60 ≈ 1.4176. M = 20,000 × 0.005833 × 1.4176 ÷ 0.4176 = $396.02/month. Total paid: 396.02 × 60 = $23,761.44. Total interest: 23,761.44 − 20,000 = $3,761.44. Stretch the same loan to 7 years and the payment drops but total interest climbs past $5,300 — cheaper monthly, more expensive loan.
Practical tips
Compare total interest + fees, never the monthly payment alone. A 1% rate difference on a 5-year $20,000 loan is worth roughly $550 — real money. And check whether extra payments are penalized; if not, even $50 extra monthly on the example above saves hundreds in interest.
The extra-payment effect
On our $20,000 / 7% / 5-year example ($396.02/month), adding just $50 extra per month — applied to principal — pays the loan off about 8 months early and saves roughly $550 in interest. Why so much leverage? Early in the loan, most of each payment is interest; shrinking principal early starves all future interest charges. The mirror lesson: front-loaded fees (origination charges added to the balance) quietly inflate P before the first payment — a "7% loan" with a $600 fee on $20,000 behaves like borrowing $20,600. Always compare offers on total interest plus fees, and ask whether extra payments reduce principal without penalty.
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