## Cost of Credit Formula

The Cost of Credit refers to the total cost of borrowing, which includes not only the interest charges but also any fees or other costs associated with the borrowing. The formula for the cost of credit can vary based on the context and the specific components of the loan or credit you’re evaluating. However, a general formula to determine the cost of credit is:

Cost of Credit = Total Amount Repaid − Principal Amount Borrowed

Where:

**Total Amount Repaid**is the sum of all payments made over the life of the loan or credit, including interest and fees.**Principal Amount Borrowed**is the initial loan or credit amount.

For more specific types of credit, such as credit cards, the cost of credit might also include annual fees, late fees, cash advance fees, and other charges.

When comparing loan offers or credit card terms, it’s useful to calculate and compare the cost of credit to understand which option is more economical in the long run.

## Example of the Cost of Credit Formula

Let’s look at an example of determining the cost of credit for a simple loan:

**Scenario**: Suppose you take out a personal loan for $10,000 with an annual interest rate of 5%. The loan term is for 3 years, and there’s also a one-time origination fee of $200.

**Step 1: Calculate the Monthly Payment**

Using the formula for an installment loan with fixed monthly payments:

\(M = P \times \frac{r(1+r)^n}{(1+r)^n-1} \)

Where:

- M = Monthly payment
- P = Principal loan amount = $10,000
- r = Monthly interest rate \((\frac{\text{annual rate}}{12}) = \frac{\text{5%}}{12} = 0.004167 \)
- n = Total number of payments (loan term in years x 12) = 3 x 12 = 36

Plugging in the numbers:

\(M = 10,000 \times \frac{0.004167(1+0.004167)^{36}}{(1+0.004167)^{36−1}} \)

\(M \approx 299.71 \)

So, the monthly payment is approximately $299.71.

**Step 2: Calculate the Total Amount Repaid**

Total Amount Repaid = M × n

Total Amount Repaid = 299.71 × 36 = 10,789.56

**Step 3: Calculate the Cost of Credit**

Cost of Credit = Total Amount Repaid + Fees − Principal Amount Borrowed

Cost of Credit = 10,789.56 + 200 − 10,000 = 989.56

In this scenario, the total cost of credit over the 3-year loan term would be $989.56, which includes the interest paid over the life of the loan and the origination fee.

Remember, this is a simplified example, and real-world scenarios might involve more complexities such as variable interest rates, additional fees, or penalties.