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Name: Thaqifah KassimClass: 205 SLComparison of Home LoansPersonal Engagement:Buying a home is an important milestone in our lives. It is an inevitable decision for most of us and is symbolic of our journeys towards taking full responsibilities over our lives. However, the cost of buying a home is often a price many cannot afford to pay at one go because they will have insufficient savings for other expenditures they will need to make at that age in their lives such as supporting a family. Therefore, many will opt to take a house loan to cover for the cost of the home. As for me, this decision of choosing a house loan is important as certain factors need to be considered before choosing a loan. As the loan is a huge amount, the period of payment will also be relatively long. Thus, the interest accumulated will also be significant. Hence, understanding the calculation of interest rate the loan offers is also an important factor to take note of. In Singapore, the loans can be taken from the various banks, the Housing Development Board (HDB) as well as from the Central Provision Board (CPF). Other factors to consider would be my income level at that age which would be about 30 years old as well as the number of dependents I would need to channel my income to. How big will the house I buy need to be? Will my income level be sufficient to support the cost of the home? Which loan will allow me to repay this debt comfortably whilst juggling other expenditures? A small number of dependents or a small income will result in me buying a smaller home and vice versa. This then affects the cost of the home and therefore the loan I will choose to take.   Income and DependentsThus, I will be making a few assumptions to set the scope of this investigation. Since my future aspirations is to work as a medical officer in future, I will be assuming that my income level is of the average Singaporean medical officer serving in the public sector which is capped at $80,000 yearly. This figure would allow me to calculate my average monthly income as shown below.Average Monthly Income = Total Annual Income ÷ 12                                         = 80,000 ÷ 12                                        = $6666.67 (to 2 d.p.)I am also planning to start a family at that age. Considering the high costs of living in Singapore, I would prefer a smaller family size, comprising of one child and my spouse thus totalling to a family size of three. These two factors are important to note as it would determine the cost of the house I can afford as well as the size needed. Assuming my spouse earns the same monthly income as me, my total monthly household income would be:Monthly Household Income = 2 x 6666.67                                             = $13,333.30   Housing OptionsSince my family size is small and my relatively young age at the point of purchase of the house, I will assume that I will be buying a brand new four room HDB flat in a non-mature estate and that I am a first-time buyer. More specifically, I will be looking at the HDB Build to Order (BTO) flat project titled Northshore Cove in Punggol. I chose this HDB project especially as it is a relatively new project, launched in February 2017. Thus, it would give the most accurate representation of the current house prices and would project more closely to price I would need to pay in future. A four room flat in Northshore Cove has a purchase price of about $257000. .    Picture A: Artist Impression of Northshore Cove       Housing Loan Options1. HDB Concessionary LoanAs mentioned, there are two different places in Singapore to obtain a housing loan. Firstly, the Housing Development Board (HDB) offers the concessionary housing loan. This loan can only be used after all the savings in my Ordinary Account in CPF is used up. I will be using the average amount of Ordinary Account savings to aid my calculations. To calculate the average amount of savings in the Ordinary Account of an average Singaporean, I will be obtaining the total amount of savings (in millions) in OAs divided by the total number of CPF members (in millions). Average OA Savings = 121,001.1 ÷ 3.78                                  = $ 32010.87                                  =$ 32000 (3sf)As the cost would be shared between my spouse’s and I’s CPF accounts, the total amount of OA savings available for usage to pay for the house should be doubled. Hence, the total savings available would be:Total OA Savings = 32010.87 x 2                            = 64021.70                           = $64 000 (3sf)This amount can be used to cover the cost of the down payment. The amount required for down payment depends on the type of loan taken. For a HDB Concessionary loan, the down payment needed would be 10% of the purchase price. Thus, the down payment I would need to pay would be as such:Down Payment = 0.1 x Purchase Price (PP)                         = 0.1 x 275000                         = $ 27 500By subtracting the amount paid for down payment from the amount available in our Ordinary Savings accounts, I am able to calculate the amount of money left to cover the rest of the purchase price of the house. However, I will still need to take into account other costs of administration and duty charges that will be covered by the OA as well. Amongst these costs include:1. Stamp Duty for Agreement of Lease(1) Refers to the tax on documents relating to the purchase or lease of a property(2)  The amount payable is as such:(a) First $180000: 1%(b) Next $180000: 2%(c) Remaining: 3%(3) Hence, the stamp duty payable for this property would be:(a) Stamp Duty = 0.01 (180000) + 0.02 (275000-180000)                   = $ 37002. Conveyancing Fee(1) Fee paid to transfer a property from one party to another(2) Conveyancing fees are calculated as such:i. First $30 000: $0.90 per $1000ii. Next $30 000: $0.72 per $1000iii. Remaining Amount: $0.60 per $1000(3) Thus, the conveyancing fees for this property would be:i. Conveyancing Fee = 0.9 (30000 ÷ 1000) + 0.72 (30000 ÷ 1000) +0.6             (215000÷1000) =  $177.603. Caveat Registration Fee(1) Fixed fee of $64.45 to protect your interest in the flatHowever, the existence of an option fee which is the fee paid when booking a flat is reimbursed if there is sufficient OA savings to cover the down payment, which is the case for me. The option fee for a four-room flat is $2000.Hence, the total extra expenses for the flat is:Total Added Expenses = 177.60 + 3700 + 64.45 – 2000                                     = $ 1942.05With this amount, I can now calculate the remaining OA savings available:Remaining OA available = 64021.70 – 27500- 1942.05                                        = 34579.70                                        = $34,580 (nearest dollar)By subtracting the remaining OA available to cover the cost of the house from the purchasing price, I can obtain the amount needed to be loaned from HDB or also known as the principal amount (PA).Principal Amount = 275000 – 34579.70                             = $ 240420The interest amount for a HDB Concessionary Loan is at 0.10% above the prevailing CPF Ordinary Account (OA) interest rate. Thus, the interest rate would be at 2.6% per annum and is based of the outstanding loan balance at the end of the month.  To calculate the repayment period, I will be making a few assumptions. Firstly, I will assume that I will spend the rest of my working life to pay for the home. This would mean that the repayment period would be from now until my retirement age which is minimally at 62 years old.  Hence, the repayment period would be as follows:Repayment Period = Retirement Age – Current Age                               = 62-30                               = 32 yearsTherefore, the total number of payments needed to be made would be the repayment period multiplied by twelve months as the payments are made monthly for 32 years. This can be seen in the equation below:Number of Payments = Repayment Period x 12 months                                  = 32 x 12                                  = 384Therefore, the amount payable each month (not including interest) would be:Amount Payable each Month=Principal Amount ÷ Number of Payments                                               = 240420 ÷ 384                                               = 626.094                                               = $ 626.10 (to nearest cent)I can now calculate the total amount of money payable after the first month including interest. As this is a concessionary loan, the interest payable is simple interest. Hence, the interest can be expressed as seen below:Interest = 0.026 (240420 – 626.1 (n-1))Where n= the month at which the loan is paidEg: first month of payment will be n=1 Thus, the interest payable after the first month is:First Month Interest =0.026 (240420- 626.1 (0))                                 = $6250.92Second Month Interest = 0.026 (240420- 626.1 (2-1))                                      = $6234.64Third Month Interest = 0.026 (240420 – 626.1 (3-1))                                   = $6218.36In an attempt to establish a pattern between these interest amounts, I tried to find the numerical relation between all three interest amounts and found that they all differ by $16.28. Difference between first and second month = 6250.92 – 6234.64                                                                      = $16.28Difference between second and third month = 6234.64 – 6218.36                                                                       = $16.28With that, I can establish that there is an arithmetic progression between the interest payable from month to month as the is a common difference of $16.28. The presence of a common difference suggests an arithmetic progression between the monthly loan amounts. This allows me to calculate the total amount of interest payable at the end of the repayment period using the arithmetic progression formula:                                                        Sn =  (2a + (n-1)(d))Where n= the month at which the loan is paid,a = the first term of the sequenceAnd d = the common difference An arithmetic progression is defined as a sequence of numbers in which each differs from the preceding one by a constant quantity. The constant quantity in this case would be the common difference of $16.28. This common difference gives rise to an important property of an arithmetic progression which is that the sum of corresponding terms from the start to the end of an arithmetic progression series is also constant. Given that the first term is a1 and the final term is an,a1 + an = a2 + an-2 = a3 + an-3 = an + a1 This can be proven using the equation below,1+2+3+…+98+99+100 = 5050Considering that there is a common difference of 1 between all the integers above, this equation is considered an arithmetic progression. We take 1, which is the first term, to be a and 100, the final term, to be n. Thus,1 + 100 = 2+99 = 3+98 = 100+1 = 101Therefore, to add the first n terms of an arithmetic progression, Sn = a1+ (a1 +d) + (a1 +2d) + … + (an + 2d) + (an + d) + anThe corresponding reverse of this equation would be,Sn = an+ (an +d) + (an +2d) + … + (a1 + 2d) + (a1 + d) + a1Adding these two expressions would give,2Sn = (a1 +an) + (a1 +an) + (a1 +an)+ … + (a1 +an)+ (a1 +an) = n (a1 +an)Therefore,Sn = n (a1 +an)    = n (a1 +(a1 + (n-1)(d)) as an= a1 + (n-1) (d)=  (2a1 +(n-1)(d)      To more specifically define this equation relative to this case, n refers to 384 months which is the last month the loan will be paid, a is $6250.92, the first month interest and d refers to $16.28, the difference between the interest amounts.Thus, the total interest payable under the HDB loan would be:Total Interest Payable = (384÷2) (2 (6250.92) + (384-1)(-16.28))                                    = $1203180Hence the total amount payable under the HDB Loan is:Total Amount Payable = Total Interest Payable + Principal Amount                                    = 1203180 + 240420                                    = $1443600Another factor to consider when opting for a HDB loan is that the option to repay this loan via CPF is available. This is an incentive as there will be lesser strain on my GIRO savings and it opens a whole pool of usually inaccessible financial resources. This allows me to channel my GIRO resources to other expenditures in life.     2. POSB Home LoanThe POSB Home Loan is an example of the various bank loans available for buying a house. An interesting concept behind this loan as compared to the HDB loan would be the 2-year cap on the floating interest rate. This would mean that for the first two years, the interest rate is capped below 1.72% pa. This figure is made up of the FHR9 (a variable) + 1.07%. The current FHR9 value is at 0.250% pa. The graph below depicts the interest rates offered over two years by POSB: Graph 1: POSB Interest Rates    When a bank loan is used to buy a home, the down payment needed is increased to 20% with 5% of this amount paid in cash and the rest in either CPF or Giro. Thus, the down payment would be as follows:Down Payment = 0.2 (257000)                          = $51400Hence, the remaining amount needed to be covered by the bank loan would be:Principal Amount = Purchase Price – Down Payment + Total Added Expenses                                = 257000 – 51400 + 1942.05                                = $207542To aid in this calculation, I will be assuming the extreme interest rates possible. Therefore, for the first two years, the interest rate will be taken to be 1.72% pa. To establish the repayment period, I will be adopting the same equation as seen previously in the HDB loan calculation.Number of Payments = Repayment Period x 12 months                                  = 32 x 12                                  = 384The interest is also assumed to be compounded as POSB is a profitable financial institution that most probably seeks to gain as much interest possible to ensure the survivability of their institution. The compound interest formula is as follows:Amount Payable = Principal Amount (1 + ) ntWhere r = Interest Rate (decimal)n = number of times compounded yearlyt = time (years)   The derivation of the compound interest formula is as follows. Firstly, let the principal amount be A. If the compound interest rate is x% annually, the final amount after a year would be (1+ times the principal amount. As such, the amount payable would increase by  times annually. Therefore, the amount payable through the years would be as follows:Year 1: A (Year 2: A ( ) = A (2Year n: A ( )n = A (nThus, the amount payable = A (n where A is the principal amount, x the interest rate and n the number of times compounded annually.Therefore, the amount payable for the first two years would be:Amount Payable = 207542 ( 1 +  ) 12(2)                                        = $214800The extreme interest rate for the remaining loan tenure would be 5% as seen in the graph. Thus, the remaining amount payable would be:Remaining Amount Payable = 207542 (1+  ) 12(30)                                                                   = $ 927245Thus, the total amount payable under this POSB loan would be:Total Amount Payable = 214800 + 927245                                    = $1142045    Conclusion HDB Concessionary LoanPOSB Home LoanInterest Rate2.6% p.a1.72% p.a  for first 2 years5% p.a for next 30 yearsType of InterestMonthly Rest BasisCompoundedMode of PaymentCompulsory to use OA savings before using GIRONot compulsory, can use GIROTotal Amount Payable$ 1443600$1142045In conclusion, I will choose to take a POSB bank loan instead of a HDB Loan. Though a HDB loan is preferred when the buyer does not have sufficient cash on hand and offers simple interest on a monthly rest basis, the final total amount payable for a HDB loan is much more than the final amount payable for the POSB Home Loan. The difference is as such:Difference = 1443600 – 1142045                 = $301 555The difference is a significant amount and can be channelled to better uses. The HDB loan also utilises majority of the OA savings I have. These savings need to be used for future expenses such as to fund my children’s university education. Thus, I would prefer to take on the bank loan to ensure that there will be sufficient savings in my OA account when the time calls for it. The interest rates I have assumed for the bank loans is also at the extreme. Thus, it is possible that the total amount payable for a bank loan can be lower than that calculated. This is in comparison to the HDB loan where the interest rate is rather fixed and yet the total amount payable is still higher than the amount payable for a bank loan.