Mr. Thompson is a CPA specializing in personal finance and debt management strategies, ensuring the calculation of total interest and debt payoff is accurate for financial planning purposes.
The **Debt Repayment Calculator** helps you analyze and plan for paying off any installment loan (like a mortgage or auto loan) by solving for the **Loan Principal ($P$)**, **Monthly Payment ($M$)**, **Annual Interest Rate ($R$)**, or **Total Interest Paid ($I_{total}$)**, provided you enter the other three variables.
Debt Repayment Calculator
*Enter any 3 values to solve for the 4th. Term will be calculated as an intermediate step.
Debt Repayment Formulas & Logic
This calculator relies on two core relationships:
1. Total Payout (TP):
$$ TP = P + I_{total} $$
2. Monthly Payment (M) vs. Principal (P) (Amortization):
$$ P = M \frac{1 - (1 + i)^{-n}}{i} \quad \text{or} \quad M = P \frac{i(1+i)^n}{(1+i)^n - 1} $$
Where $n$ is the total number of payments (months) and $i = R / 1200$ (monthly rate).
Formula Source: Investopedia (Loan Repayment)
Variables Explained
- $P$ (Loan Principal): The original amount borrowed. (F in input map)
- $M$ (Monthly Payment): The fixed amount paid each month. (P in input map)
- $R$ (Annual Interest Rate): The annual percentage rate of the loan. (V in input map)
- $I_{total}$ (Total Interest Paid): The cumulative amount of interest paid over the life of the loan. (Q in input map)
Related Calculators
Plan your debt repayment and savings goals using related financial tools:
- Amortization Period Calculator
- Monthly Payment Calculator
- Future Value Calculator
- Mortgage Payoff Calculator with Extra Payments
What is Debt Repayment?
**Debt Repayment** refers to the systematic process of paying back a borrowed sum (the principal) plus the associated costs (interest) over a specific period. For installment loans like mortgages, this is governed by an **amortization schedule**, where each fixed monthly payment ($M$) consists of two parts: a portion applied to the interest and a portion applied to the principal.
In the initial years of an amortized loan, the majority of the monthly payment goes toward interest. As the loan matures and the principal balance decreases, a larger portion of the payment goes toward reducing the principal. The **Total Interest Paid ($I_{total}$)** is a critical metric, as it represents the true cost of borrowing the funds and is calculated as the difference between the Total Payout ($M \times n$) and the original Principal ($P$).
Effective debt repayment planning often involves analyzing different scenarios—such as making extra payments or refinancing—to minimize the total interest paid and accelerate the payoff timeline. This calculator provides the underlying relationship between the four key financial variables used in such strategic planning.
How to Calculate Total Interest Paid (Example)
Let’s find the total interest paid for a \$100,000 loan at 5.0% APR with a \$662.90 Monthly Payment (M).
- Determine the Loan Term (T) and Total Payments (n):
Using the amortization formula with the given P, M, and R, the term is calculated as $T \approx 20$ years (240 months).
- Calculate the Total Payout (TP):
$$ TP = M \times n = \$662.90 \times 240 \approx \$159,096 $$
- Solve for Total Interest Paid ($I_{total}$):
$$ I_{total} = TP – P = \$159,096 – \$100,000 $$
- Conclusion:
The Total Interest Paid is \$59,096. This is the cost of borrowing the \$100,000 over 20 years.
Frequently Asked Questions (FAQ)
The total interest paid is directly related to the loan term. A longer term means more total payments, resulting in significantly higher cumulative interest, even if the monthly payment is lower.
Q: What is the benefit of an Amortization Schedule?The Amortization Schedule breaks down every single monthly payment into the exact amount allocated to interest and the exact amount allocated to principal, showing the loan balance decrease over time.
Q: Can I use this calculator for variable-rate loans?This calculator is based on fixed-rate amortization formulas. While it can estimate total interest for a variable-rate loan, the result will only be accurate for the initial rate period, as the rate change will alter future payments and total interest.