Ms. Vance is a certified mortgage analyst specializing in loan amortization and long-term debt cost management, ensuring all calculations reflect accurate total interest paid figures.
The **Interest Paid Calculator** helps you analyze the true cost of a loan by solving for any missing variable: Total Interest Paid (I), Principal Amount (P), Annual Interest Rate (R), or Loan Term (T). Enter any three known values below to solve for the unknown fourth.
Total Interest Paid Calculator
*Assumes monthly payments (12 compounding periods per year).
Interest Paid Formulas
The calculation is based on the Monthly Payment ($M$) derived from the amortization formula.
$$ M = P \frac{i(1+i)^n}{(1+i)^n - 1} $$
The Total Interest Paid (I) is then:
$$ I = (M \times n) - P $$
Formula Source: Investopedia (Total Interest Paid)
Variables Explained
- I (Total Interest Paid): The cumulative amount of interest paid over the life of the loan. (F in input map)
- P (Principal Amount): The initial amount of money borrowed. (P in input map)
- R (Annual Interest Rate): The annual stated rate used to calculate interest charges. (V in input map)
- T (Loan Term in Years): The duration of the loan. (Q in input map)
- *$i$ (Monthly Rate) = R / 1200; $n$ (Total Periods) = T x 12
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What is Total Interest Paid?
**Total Interest Paid** represents the true financial cost of borrowing the principal amount (P) over the entire duration of the loan (T). It is a vital metric for borrowers as it often far exceeds the original principal, highlighting the long-term impact of the interest rate (R) and the loan term (T).
The total interest paid is derived from the loan’s amortization schedule. Every monthly payment (M) is split into a portion for interest and a portion for principal. Over the life of the loan, the interest payments are summed up, and this total is equal to the cumulative monthly payments minus the original principal borrowed: $I = (\sum M) – P$.
Analyzing the total interest paid is essential when comparing loan offers. A seemingly small difference in the Annual Interest Rate (R) or extending the Loan Term (T) by a few years can drastically increase the total interest paid, representing tens of thousands of dollars in extra cost. This calculator allows users to quickly visualize that long-term expense.
How to Calculate Total Interest Paid (Example)
Let’s calculate the **Total Interest Paid (I)** for a \$100,000 loan at 6% interest over 15 years.
- Determine Parameters:
$P = \$100,000$. $R = 6\%$. $T = 15$ years. Monthly rate $i = 0.06/12 = 0.005$. Total payments $n = 15 \times 12 = 180$.
- Calculate Monthly Payment ($M$):
Using the formula: $M = \$100,000 \frac{0.005(1.005)^{180}}{(1.005)^{180} – 1} \approx \$843.86$.
- Calculate Total Payments Made:
Total Paid: $\$843.86 \times 180 = \$151,894.80$.
- Calculate Total Interest Paid (I):
$I = \text{Total Paid} – P = \$151,894.80 – \$100,000.00 = \$51,894.80$.
- Conclusion:
The Total Interest Paid (I) is approximately \$51,894.80.
Frequently Asked Questions (FAQ)
The two main ways are: 1) Refinancing to a lower Annual Interest Rate (R), and 2) Shortening the Loan Term (T). Additionally, making extra principal payments reduces the principal balance sooner, leading to less interest accrued over time.
Q: Does the compounding frequency matter?Yes. Although most mortgages compound monthly, if a loan compounded daily instead of monthly, it would result in a slightly higher total interest paid due to the interest being calculated and added more frequently.
Q: How much interest do I pay in the first few years?Mortgage payments are front-loaded with interest. In the early years of the loan, the majority of your monthly payment goes toward interest, and only a small portion goes toward paying down the Principal (P). The balance shifts toward principal as the loan matures.
Q: Is Total Interest Paid the same as APR?No. Total Interest Paid is the cumulative dollar cost over the entire life of the loan. APR (Annual Percentage Rate) is a percentage rate that reflects the total yearly cost, including certain mandatory fees, expressed as a rate.