Loan Interest Multiplier

What "interest multiplier" means

Two related ratios both get called the "interest multiplier" in casual usage; the calculator surfaces both explicitly to avoid confusion. The Interest-to-Principal Ratio is total interest paid divided by the original principal — a value of 0.93 means the borrower pays an additional 93% of the loan amount in interest over the life of the loan. The Total Repayment Multiplier is total amount paid (principal + interest) divided by the original principal — for the same loan, that value is 1.93, meaning the borrower pays 1.93 times the principal back in total. They differ by exactly 1; both are valid ways to express the same underlying cost.

How to use it

Enter the loan amount, the annual interest rate, and the loan term in years. The calculator returns total interest paid, the monthly payment, total amount repaid, both ratio expressions, and a 15-year alternative scenario showing the monthly payment and the interest savings if the loan were structured at 15 years instead. The currency selector at the top of the calculator changes formatting throughout — the math itself is currency-neutral.

Worked example

Picture a 200,000 loan at 5% APR over 30 years (currency follows the selector). The standard amortisation formula gives a monthly payment of about 1,073.64, total amount repaid over the term of about 386,511.57, and total interest of 186,511.57. As ratios: Interest-to-Principal is 0.93× (interest is 93% of principal); Total Repayment Multiplier is 1.93× (total payback is 1.93× principal). Switching to a 15-year term at the same rate raises the monthly payment to about 1,581.59 but cuts total interest to about 84,686 — saving roughly 101,826 in lifetime interest at the cost of a higher monthly payment.

How the math works

Monthly payment = P × r × (1+r)ⁿ ÷ ((1+r)ⁿ − 1) where P is principal, r is the monthly rate (annual ÷ 12 ÷ 100), and n is months. Total paid = monthly payment × months. Total interest = total paid − principal. Interest-to-Principal Ratio = total interest ÷ principal. Total Repayment Multiplier = total paid ÷ principal. The 15-year alternative uses n = 180 with the same rate.

Why monthly payment hides total cost

Borrowers tend to compare loans on monthly payment because that's what hits the bank account each cycle. The interest multiplier is one way to keep total cost in view alongside the monthly figure. A loan with a slightly lower monthly payment over a longer term often produces a much higher Interest-to-Principal Ratio, sometimes meaningfully more than 1.0 — the borrower pays more in interest than the original loan amount. Running the calculator at different terms and rates usually surfaces this trade-off more directly than reading any general statement.

Small rate differences, large lifetime impact

Because interest compounds across the term, even a small change in rate produces a noticeably different lifetime interest figure on a long-term loan. As an orientation, on a 30-year mortgage a half-percentage-point rate change typically shifts total interest by 5-15% depending on the principal and starting rate. The calculator's sensitivity to a 0.5pt rate change is usually clearest by trying it directly with the user's own numbers.

What this calculator doesn't capture

The model assumes a fixed rate for the full term, equal monthly payments, no fees or insurance products, and no prepayment. Variable-rate behaviour, arrangement and origination fees, prepayment penalties or rebates, points paid up front, escrow for taxes and insurance (typical on US mortgages), and tax treatment that varies by country and product type are all outside this calculation. The figures are an estimate of the headline lifetime cost based on the three inputs entered.