When buying a home in Singapore, most people choose to apply for a mortgage loan from a bank. After securing a mortgage, you need to pay a fixed amount to the bank each month as repayment. But how do we calculate the monthly mortgage payment amount?
This is a crucial question because the monthly mortgage payment (which we’ll call ‘monthly installment’) determines our affordability for buying a home. Of course, we can easily calculate it using a mortgage calculator. However, many people still don’t understand how this repayment amount is calculated. This article will help you clarify the issue from the perspective of loan principal and interest. Attention, class: the math lesson is about to begin!
Table of Contents
What is the Formula for Calculating Monthly Payments?
For those who like math, the mortgage repayment formula is not that complicated. Please remember: this does not take into account floating interest rates. The interest rate may change.
First, we need to understand what the formula represents:
- r = Annual interest rate / 12 (months)
- P = Loan principal (initial balance)
- n = Total number of repayments: If you make one mortgage payment per month for 25 years, then n = 25 * 12 = 300
The formula is as follows:
Monthly Payment = P * [ (r(1+r)^n) / ((1+r)^n-1) ]
If we want to calculate the repayment for an average mortgage, it might look like this:
r = 0.033 / 12 = 0.00275
P = $350,000
n = 25 * 12 = 300 (one payment per month for 25 years)
This is a $350,000 mortgage with an annual interest rate of 3.3% over a 25-year term.
Let’s plug these numbers into the formula:
Monthly Payment = 350000 * [ (0.00275(1+0.00275)^300) / ((1+0.00275)^300-1) ]
We need to simplify the formula:
Monthly Payment = 350000 * [ (0.00275(2.27930)) / (2.27930 – 1) ];
Monthly Payment = 350000 * (0.00627 / 1.2793);
Monthly Payment = 350000 * 0.00490
The final calculation is:
Monthly Payment = 1715
If you’d like to perform calculations based on your own situation, you can also use our mortgage calculator to view a detailed loan amortization schedule.
Why is the Monthly Mortgage Payment so Complicated?
Banks need to make money from lending, and that’s what the interest they charge on loans is for. In essence, mortgage interest is the fee the bank charges you for borrowing money.
If repayments didn’t consider the factor of time, calculating mortgage payments would be very easy. Unfortunately, the cost of time accounts for a significant portion.
This “time value of money” is what we call “compound interest.” Albert Einstein called compound interest “the most powerful force in the universe.” If you borrow $10,000 at a 2% simple interest rate for 10 years, you would pay $200 in interest each year—super simple, right?
However, when borrowing with compound interest, we must calculate the interest on the remaining outstanding balance with each repayment.
Mortgages in Singapore use compound interest, and the mathematical formula is calculated as follows:
Borrowing $10,000 at 2% interest for 5 years results in an annual repayment of $2,121.58.
- In the first year, you owe the bank $10,000. The first year’s repayment is $2,121.58. Based on the 2% interest rate, $200 of this is interest payment, and the remaining $1,951.58 is principal repayment. (The principal is the amount you initially borrowed.)
Why do we need to distinguish between the interest and principal in the monthly payment? The interest goes directly to the bank, while the amount owed next year is reduced by the principal already paid: $10,000 – $1,951.58 = $8,078.42.
- In the second year, the amount you owe the bank is less ($8,078.42). You still pay $2,121.58, but this time you pay less interest—because you’re paying 2% of $8,078.42, which is $161.57. The rest ($1,960.02) goes towards the principal. Now you owe the bank $6,118.40.
- In the third year, you make the same payment of $2,121.58. This time, you pay 2% interest on $6,118.40, which is $122.37. You now owe the bank $4,119.18.
- In the fourth year, repeat the process: 2% of $4,119.18 is $82.38. Now you owe the bank $2,079.98.
- In the fifth year (the final year!), you make the last payment: $2,079.98 plus 2% interest, totaling $2,121.58.
Mind-boggling, right? This is also why the interest rate is so important: if your interest rate in the above example was 5%, you would pay nearly $1,000 more in interest. Imagine: for a $1 million mortgage over 25 years, how much interest would you pay? It would surely be a painfully large number.
How Do Floating Interest Rates Work?
So far, we’ve been discussing fixed interest rates, where the rate remains the same.
If you get a mortgage with a floating interest rate, your rate can change (it all depends on the bank). Typically, this variable rate is pegged to the Singapore Overnight Rate Average (SORA), floating on top of SORA.
If you thought compound interest was painful for borrowers, then floating rates are the devil. This is because they greatly increase the complexity of the calculation. Most mortgages have a fixed rate for a short period: usually, the rate is fixed for the first 2-5 years. When your mortgage term extends beyond this lock-in period, your loan will switch to a floating rate, and your monthly payment amount could change every month!
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