The math behind: HDB vs Bank Housing Loan
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Introduction
In our previous article, we shared our findings on the differences between HDB and bank loans in particular how much you would be paying in total (including interest) and the amount you would have accumulated at the end of the loan tenure. If you have yet to read that article, you can check it out here:
In this article, we will provide a more detailed explanation of how we derived these numbers and what are some of the mistakes we’ve made so that you can do the math yourself.
Key columns
These are the columns that we have that are consistent throughout the different options that we painted out in the previous article. Starting from the left:
- Tenure years. This column shows the number of years you need to pay for your mortgage loan. Since we are assuming that you are taking the Staggered downpayment scheme, the loan tenure year only starts when you receive the key to your flat. If you do not wish to opt-in for this scheme, then your tenure years will be the same as the “year” 's column
- Years. The count of the year starting at Year 0 illustrate that the starting balance for all 4 options is consistent for a fair comparison.
- OA (invested). This column is to illustrate a situation where you invest your CPF Ordinary Account (OA) balance. We understand that there are some restrictions in place when it comes to investing with your OA. For example, you need to have a minimum of $20,000 in your OA to start investing. This restriction is accounted for in our calculation. On top of that, due to the limited amount of investment options using our OA and also the nature of the purpose of our OA monies, we chose to compound it only at a 4% interest return.
- OA (not invested). This column is pretty straightforward, it is the balance of your OA compounded at 2.5% p.a., add the new yearly contribution and minus off the mortgage payment.
There are a few assumptions made in this equation. Firstly, we disregard the miscellaneous payment from OA such as the Dependent Protection Scheme (DPS). Secondly, we ignore the way CPF actually calculates your interest. From the CPF website, “ CPF interest is computed monthly. It is then credited to your respective accounts and compounded annually.” Lastly, CPF actually gives us more than 2.5% for the first $20,000 in our CPF OA, you can find out more here. Although these assumptions will affect the actual value for this simulation, they are held constant across all options. So it will not affect the conclusion that we make in the article.
5. Investment. This column is here because the bank loan has a 5% downpayment that is required to be paid by cash. For a fair comparison, we need to include this under the HDB option as well to avoid any biases. In this investment column, we decided to compound at 6% p.a. slightly more than the OA (invested) because it has more flexibility in what you can invest and also the annualised return for S&P 500 is averaged at about 10–11%, so we further tuned it down to be a little more conservative.
6. Payment to flat. This column basically shows the total annual mortgage payment. The value in this column is held constant through each option. For example, if your monthly mortgage payment is $2,000 per month then the annual mortgage payment would be
$2,000 *12 = $24,000
Except at the start of the year where the downpayment is involved and at the last year of the loan tenure, where the remaining flat balance is less than your annual mortgage payment. When that is the case, you will just pay the remaining balances.
7. Flat balance. This column shows the mortgage amount left, except during the downpayment years. This is the equation that we use for this column:
Final Amount
Total Paid
The total paid column is the sum of the “Payment to flat” column. In other words, this amount represents the total mortgage paid (including interest). The total amount would vary based on the type of loan you pick and the monthly repayment amount.
Asset (OA without Investment)
This amount is calculated by adding the “OA (not invested)” with “investment 6%” at the 30th year mark.
Asset(OA without Investment ) = OA(not invested) + Investment
This amount is meant to illustrate the total balance you would have at the end of 30 years if you did not invest your OA and invested your cash.
Asset with OA invested
This amount is calculated by adding “OA(invested)” with “investment 6%”.
Asset with OA invested = OA(not invested) + Investment
The asset with OA invested amount shows the total asset you would have at the end of 30 years when you invest your OA. This is to make a comparison between investing and not investing OA to highlight its importance.
Key things to note
Over time, the process of buying a house alongside the terms and conditions for a housing loan has become complex. In our initial phase of the calculation, we overlooked the clause that buyers going for an HDB loan can only retain a total of $20,000 in each of their OA before the HDB loan board decides to give the loan. You can learn more about this clause here under the use of the CPF savings option. This clause will mostly affect couples who already have been working for a while now. For those who have just started working, this might not be as relevant to you.
In theory, investing to get the most out of your money and leverage on compound interest sounds good. But in reality, investment is hardly a smooth ride, there will be turbulence along the way that may deviate from the simulation. We are not saying this to stop you from investing, but rather to understand that investing is not guaranteed.
Conclusion
In this article, we covered the calculations we did behind our earlier post. We acknowledge that the way we calculate these numbers may not be the best way to do so. But it is enough for us to understand the options we have in hand. After all, when it comes to modelling, there is a saying “all models are wrong but many are useful”. You can’t simulate everything to precision, there are always tradeoffs and assumptions to make. The key is to make logical assumptions and understand the implication of making them.
If you wish to find out how you can invest your CPF OA you can sign up via this form and our trusted colleagues will be in contact with you. Alternatively, you can simply drop us a DM on Instagram to find out the details.
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