Financial Expertise & Validation: This calculator uses standard time-value-of-money formulas.
Use this powerful tool to quickly determine the total interest cost and monthly payments for any amortized loan, helping you plan your financial future accurately.
Amortized Loan Interest Costs Calculator
Total Interest Paid
$0.00Monthly Payment:
Total Cost:
Amortized Loan Interest Costs Formula
The calculation of interest costs relies on first determining the fixed monthly payment (M) using the standard amortization formula:
$$M = P \left[ \frac{r(1+r)^t}{(1+r)^t - 1} \right]$$
Once M is calculated, the total interest paid (I) is found by:
$$I = (M \times t) - P$$
Formula Source:
Investopedia: Amortization Schedule,
The Balance: Loan Payment Formula
Variables Explained
Understanding the variables used in the calculator is crucial for accurate results:
- P (Loan Principal): The initial amount of money borrowed.
- R (Annual Interest Rate): The annual percentage rate charged by the lender (used to derive $r$).
- N (Loan Term in Years): The length of time over which the loan must be repaid (used to derive $t$).
- $r$ (Monthly Interest Rate): The annual rate divided by 12 and 100 ($R / 1200$).
- $t$ (Total Payments): The loan term in years multiplied by 12 ($N \times 12$).
Related Calculators
Explore these other useful financial tools:
- Mortgage Refinance Calculator
- Debt Consolidation Savings Calculator
- Compound Interest Future Value Calculator
- Personal Loan Monthly Payment Calculator
What is Amortized Loan Interest Costs?
Amortized loan interest cost is the total amount of money paid to the lender beyond the principal amount over the entire life of the loan. An amortized loan is structured so that each payment consists of both principal and interest. In the early stages of the loan, a larger portion of the payment goes toward interest, while in the later stages, a larger portion goes toward reducing the principal balance.
Understanding this total cost is vital for borrowers because it represents the true expense of borrowing. For example, a $200,000, 30-year mortgage at 5% interest results in over $186,000 in interest costs alone. This calculation helps in making informed decisions about whether a loan term or rate is financially acceptable.
The term “amortized” simply means the loan’s balance is paid down gradually over time according to a set schedule. Unlike simple interest loans, the interest on an amortized loan is calculated on the remaining balance, ensuring the debt is fully paid off by the final scheduled payment.
How to Calculate Amortized Loan Interest Costs (Example)
Let’s use an example loan of a $10,000 Principal, 5% Annual Rate, over 5 Years:
- Determine Monthly Rate ($r$): Divide the annual rate by 1200. $5\% / 1200 = 0.0041667$.
- Determine Total Payments ($t$): Multiply the term in years by 12. $5 \text{ years} \times 12 = 60 \text{ payments}$.
- Calculate Monthly Payment ($M$): Apply the amortization formula. $$M = 10000 \left[ \frac{0.0041667(1+0.0041667)^{60}}{(1+0.0041667)^{60} – 1} \right] \approx \$188.71$$
- Calculate Total Payments: Multiply the monthly payment by the total number of payments. $\$188.71 \times 60 = \$11,322.60$.
- Calculate Total Interest Paid ($I$): Subtract the original principal from the total payments. $\$11,322.60 – \$10,000 = \$1,322.60$.
Frequently Asked Questions (FAQ)
Amortized interest is calculated on the remaining principal balance, meaning the interest component of your payment decreases over time. Simple interest is often calculated only on the original principal amount for the entire duration of the loan, though some products use simple interest calculated daily on the outstanding balance.
The two biggest factors are the Annual Interest Rate and the Loan Term. Even a small increase in the interest rate or extending the loan term by a few years can drastically increase the total interest paid over the life of the loan.
Yes. Since interest is calculated on the remaining principal balance, making extra payments specifically toward the principal reduces the balance faster. This immediately lowers the amount of interest charged in all subsequent periods, saving you significant money.
No. The Total Interest is the cost of borrowing (the money paid above the principal). The Total Cost is the sum of the Loan Principal plus the Total Interest Paid. This represents the full cash outflow for the borrower.