Sarah Jenkins is a CFP professional specializing in mortgage amortization and total cost of borrowing, ensuring precise calculation of total interest paid over the life of a loan.
Use the **Amortization Interest Calculator** to determine the total interest paid, the principal borrowed, the annual rate, or the loan term. Enter any three of the four core variables for a fixed-rate loan, and the calculator will solve for the missing fourth item.
Amortization Interest Calculator
*Enter any 3 values to solve for the missing 4th item. Assumes monthly compounding.
Amortization Interest Formula
The calculation is derived from the monthly payment (M) formula and the relationship $I = (M \times N) – P$.
Monthly Payment (M) Formula:
$$ M = P \frac{i(1+i)^n}{(1+i)^n - 1} $$
Total Interest (I) Formula:
$$ I = \left[ P \times \frac{i(1+i)^n}{(1+i)^n - 1} \times n \right] - P $$
Formula Source: Investopedia (Amortization)
Variables Explained
- **Principal Loan Amount ($P$):** The initial amount borrowed. (F in input map)
- **Annual Interest Rate ($R$):** The stated yearly rate of interest. (P in input map)
- **Loan Term (Years) ($T$):** The length of time over which the loan is repaid. (V in input map)
- **Total Interest Paid ($I$):** The cumulative amount of interest paid over the entire life of the loan. (Q in input map)
Related Calculators
Analyze your loan costs and payments with these related tools:
- Monthly Payment Calculator
- Loan Principal Calculator
- Effective Interest Rate Calculator
- Mortgage Payoff Date Calculator
What is Amortization Interest?
Amortization interest refers to the total amount of interest that accrues and is paid on a loan from the start date until the final payment. In an amortized loan (like a mortgage), the monthly payment remains constant, but the allocation between principal repayment and interest changes over time. In the early stages, most of the payment goes toward interest, while in the later stages, most goes toward principal.
The total interest paid is the true cost of borrowing the funds. It is calculated by summing up all the monthly payments made over the life of the loan and subtracting the original principal loan amount. This figure is critical for borrowers to understand the true financial impact of their loan term and interest rate choice.
The longer the loan term and the higher the interest rate, the greater the total interest paid. Analyzing this metric often drives decisions toward shorter loan terms (e.g., 15-year mortgages) or making extra principal payments to reduce the overall cost of borrowing significantly.
How to Calculate Total Interest Paid (Example)
Scenario: Principal P = \$100,000, Annual Rate R = 5%, Term T = 15 years.
- Calculate Monthly Rate ($i$) and Total Payments ($n$):
$i = 0.05 / 12 \approx 0.0041667$.
$n = 15 \times 12 = 180$ months.
- Calculate Monthly Payment ($M$):
Using the PMT formula, $M \approx \$790.79$.
- Calculate Total Payments Made:
Total Payments = $M \times n = \$790.79 \times 180 = \$142,342.20$.
- Calculate Total Interest Paid ($I$):
$I = \text{Total Payments} – P = \$142,342.20 – \$100,000 = \$42,342.20$.
Frequently Asked Questions (FAQ)
A longer loan term (e.g., 30 years vs. 15 years) significantly increases the total interest paid because you are accruing interest on the remaining principal balance for a much longer period of time.
Q: Is the total interest tax deductible?Mortgage interest may be tax deductible, subject to annual limits and IRS rules. This deduction reduces your taxable income, thereby lowering your effective cost of borrowing.
Q: What is the fastest way to reduce total interest paid?The fastest way is by making extra principal-only payments. Because interest is calculated on the remaining balance, reducing the principal balance earlier drastically reduces the amount of interest that accrues over the loan’s lifetime.