How to Calculate Monthly Repayment of a Loan

Calculating the monthly repayment of a loan involves understanding the loan amount, interest rate, and repayment term. In essence, it boils down to a mathematical formula used to determine how much you need to pay each month to repay the loan in full by the end of the term. The formula used for this calculation is derived from the amortization concept, which spreads out the loan payments over time.

To calculate the monthly repayment, you'll need to use the following formula:

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

Where:

• $M$M = Monthly repayment amount
• $P$P = Principal loan amount
• $r$r = Monthly interest rate (annual interest rate divided by 12)
• $n$n = Total number of payments (loan term in years multiplied by 12)

Let's break down the components of this formula and understand how each one impacts your monthly repayment.

Principal Loan Amount (P): This is the initial amount borrowed. For example, if you take out a loan of $100,000, your principal is $100,000. The larger the principal, the higher the monthly payments will be.

Monthly Interest Rate (r): This is calculated by dividing the annual interest rate by 12. For instance, if the annual interest rate is 6%, the monthly interest rate will be $\frac{6\%}{12}=0.5\%$126%​=0.5% or 0.005 in decimal form.

Total Number of Payments (n): This is the total number of monthly payments you will make over the life of the loan. If you have a 30-year mortgage, you will make $30\times 12=360$30×12=360 monthly payments.

Example Calculation:

Suppose you borrow $200,000 at an annual interest rate of 4% for a term of 30 years. To find the monthly repayment:

1. Convert the annual interest rate to a monthly interest rate: $r=\frac{4\%}{12}=0.003333$r=124%​=0.003333

2. Calculate the total number of payments: $n=30\times 12=360$n=30×12=360

3. Use the formula: $M=\frac{200,000\cdot 0.003333\cdot (1+0.003333{)}^{360}}{(1+0.003333{)}^{360}-1}$M=(1+0.003333)360−1200,000⋅0.003333⋅(1+0.003333)360​

After performing the calculation:

$M\approx \frac{200,000\cdot 0.003333\cdot 3.243}{2.243}\approx 954.83$M≈2.243200,000⋅0.003333⋅3.243​≈954.83

So, your monthly repayment would be approximately $954.83.

Understanding Amortization:

Amortization is the process of spreading out a loan into a series of fixed payments over time. Each payment covers both the interest expense and a portion of the principal. Initially, a larger part of your payment goes toward interest, but over time, more goes toward reducing the principal.

Creating an Amortization Schedule:

An amortization schedule details each payment's breakdown between interest and principal. It also shows the remaining balance after each payment. This schedule helps borrowers understand how their payments impact the loan balance over time and can be created using online calculators or spreadsheets.

Using Loan Calculators:

Online loan calculators simplify this process by allowing you to input your loan amount, interest rate, and term, and they automatically provide your monthly repayment amount. These tools are convenient for quick calculations and help you explore different loan scenarios.

Impact of Loan Term on Repayments:

The length of your loan term significantly affects your monthly repayments. Shorter terms mean higher monthly payments but less interest paid over the life of the loan. Conversely, longer terms reduce monthly payments but increase the total interest paid.

Prepayment and Its Benefits:

Making additional payments or paying off your loan early can save you money on interest. Prepaying reduces the principal balance faster, which decreases the amount of interest charged over time. This strategy can shorten the loan term and lower the total interest paid.

Conclusion:

Calculating monthly loan repayments involves understanding the key components of your loan and using the appropriate formula. By grasping how each factor affects your payments and utilizing tools like amortization schedules and online calculators, you can manage your loan effectively and make informed financial decisions.