Understanding Loan Calculation: Formula and Example

 

Introduction
Calculating a loan can seem daunting, but understanding the formula and how to apply it can simplify the process. Knowing how to calculate your loan payments helps you make informed financial decisions. So, what is the loan calculation formula, and how can you use it? Let’s dive in!

1. Loan Calculation Formula
The formula for calculating monthly loan payments is based on the loan amount, the interest rate, and the loan term. The most commonly used formula is:

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

Where:

• $M$ = monthly payment
• $P$ = principal amount (the initial loan amount)
• $r$ = monthly interest rate (annual interest rate divided by 12 months)
• $n$ = number of payments (loan term in months)

2. Example Calculation
Let’s say you want to borrow Ksh 100,000 for a car loan with an annual interest rate of 10% for 5 years. Here’s how to calculate your monthly payment.

• Step 1: Identify the Variables

  • Principal ($P$): Ksh 100,000
  • Annual Interest Rate: 10% (0.10)
  • Loan Term: 5 years

• Step 2: Convert Annual Interest Rate to Monthly

  • Monthly Interest Rate ($r$) = Annual Interest Rate / 12
    $r = 0.10 / 12 = 0.00833$

• Step 3: Calculate Total Number of Payments

  • Loan Term in Months ($n$) = 5 years × 12 months/year
    $n = 5 \times 12 = 60$

• Step 4: Plug the Values into the Formula

$$M = 100,000 \frac{0.00833(1 + 0.00833)^{60}}{(1 + 0.00833)^{60} - 1}$$

• Step 5: Calculate the Components

  • Calculate $(1 + r)^n$:
    $(1 + 0.00833)^{60} \approx 1.48985$

• Step 6: Complete the Calculation

$$M = 100,000 \frac{0.00833 \times 1.48985}{1.48985 - 1}$$ $$M \approx 100,000 \frac{0.01241}{0.48985} \approx 2,537.43$$

So, the monthly payment would be approximately Ksh 2,537.43.

3. Total Cost of the Loan
To find the total cost of the loan, multiply the monthly payment by the number of payments:

$$\text{Total Cost} = M \times n$$ $$\text{Total Cost} = 2,537.43 \times 60 \approx Ksh 152,246.00$$

4. Total Interest Paid
To calculate the total interest paid over the life of the loan:

$$\text{Total Interest} = \text{Total Cost} - P$$ $$\text{Total Interest} = 152,246.00 - 100,000 \approx Ksh 52,246.00$$

Conclusion
Understanding how to calculate your loan payments using this formula allows you to plan your finances better and make informed borrowing decisions. Have you calculated your loan payments before, or do you have questions about the process?