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Join us | Login for Financial Advisors | SMS us at +65 – 9782 - 8606Home Loan | Commercial Loan | Refinance Loan | *Financial Planning | *Insurance
Home Loans With Different Rests: Computing Their Effective Rates
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• Nominal interest rate does not reflect the true cost of borrowing.
Financial institutions use different reference rates to calculate the cost of borrowing to customers.
• In Singapore, banks can use the effective interest rate or the nominal rate.
For licensed moneylenders they are mandated by law to show the effective interest rate.
So
But
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Elsewhere in the world, banks may use the nominal rate per annum (p.a.).
For example, in Canada, Hong Kong, UK and US it is known as the Annual Percentage Rate (APR). In Australia, borrowing costs are reflected to borrowers in the Comparison Rate which takes into account the "hidden" costs like the upfront fees and charges on top of the interest rate and frequency of repayments.
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Back to Singapore, it is not legislated that banks use the effective rate on their loans.
However, we are going to calculate the effective rate for mortgages on different rests, but with monthly installments.
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Equivalent Nominal Rate (ENR)
To make a comparison among housing loans with different rests, with the same number of installment periods
We first have to find the Equivalent Nominal Rate (ENR) per annum.
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Firstly, what is the present value factor (PVF) of an annuity?
In mathematical notation it is defined as
Present Value Factor (PVF )=(1−(1+rn
(m)
m)−my
)÷r n
(m)
mrn
(m) :nominal rate or the ENRm:number of compounding per year
y :number of years
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Furthermore, we have
PVF= principalinstalment
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Finding ENR using ExcelExcel Function – RATE
RATE will return , ENR is then m*RATE
RATE (NPer, PMT, PV, FV, Type, Guess): The nominal interest rate per period for an annuity
rn(m)
m
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Finding ENR using Excel.
NPer (Required): Total number of compounding periods or payment periodsPMT: (Required): Total payment (principle and interest) payable for that compounding period PV: (Required): Present value of the loan FV: Loan amount outstanding after all payments have been made.If this variable is omitted, Excel will assume the default value of 0.
Type: The timing of the payment. It can be either 0 or 1. If this variable is omitted, Excel will assume the default value of 0.
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Finding ENR using Excel
Explanation Value
Payments are due at the end of the period. (default) 0Payments are due at the beginning of the period. 1
Guess: Your guess of what RATE is. If omitted, it is assumed to be 10%.
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Using RATE
RATE is independent of the loan amount and installment in each period.
Meaning, RATE will be the same for loans with the same number of payment periods and nominal interest rate per annum.
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Using RATE
Loan A
Loan Quantum = S$1 million Loan Tenure = 20 years Interest Rate = 10% p.a. Annual Rest with Monthly RepaymentsNumber of Payment Periods = 12 * 20 = 240Monthly Installment for the First Year = $ 9,788.30
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Using RATE
Loan B
Loan Quantum = S$5 million Loan Tenure = 20 years Interest Rate = 10% p.a. Annual Rest with Monthly RepaymentsNumber of Payment Periods = 12 * 20 = 240Monthly Installment for the First Year = $ 48,941.51
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Using RATE
Enter the syntax as shown in Table 1:
Table 1
For both loans, the RATE will return 0.83%. The ENR per annum is then 12*0.83% = 10.21%.
=RATE (240, 9788.3, -1000000) Loan A=RATE (240, 48941.51, -5000000) Loan B
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How To Compute The ENR For Loans With Different Rests, But All With Monthly Repayments.
ENR for XX-rest Loans with Monthly Installment
We will rely on the loan with the next parameters
Loan Quantum = S$1 million Loan Tenure = 20 years Interest Rate = 10% p.a.
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Table 2: Monthly Installment for the First Year
The monthly payment amount for the three rests
Monthly Payment) ( $
9,506.0 Daily Rest
9,650.2 Monthly Rest
9,788.3 Annual Rest
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Enter the below syntax to find the ENR,
Table 3Syntax
=12 *RATE (240, 9506.0, -1000000)
Daily Rest
=12 *RATE (240, 9650.2, -1000000)
Monthly Rest
=12 *RATE (240, 9788.3, -1000000)
Annual Rest
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And Excel will yield the following ENR based on monthly rest.
We just obtained the nominal rate based on monthly rest for the daily-, monthly- and annual-reducing loans.
We need to convert the interest to a common basis in order to carry out fair comparison.
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Table 4
ENR )%(9.78 Daily Rest
10.00 Monthly Rest
10.21 Annual Rest
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Going a step further, we will also like to find out the effective interest rate per annum.
Table 5: shows the syntax to enter in Excel
Syntax
=EFFECT (9.78%, 12) Daily Rest
=EFFECT (10%, 12) Monthly Rest
=EFFECT (10.21%, 12) Annual Rest
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Finally, we will be able to compare fairly the true cost of borrowing.
As expected the cost increases as the rest becomes shorter
Hence the daily-reducing loan has the lowest effective interest rate.
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Table 6: Effective Interest Rate (%)
Effective Interest Rate%( )
10.23 Daily Rest
10.47 Monthly Rest
10.70 Annual Rest
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About Property Buyer Mortgage Consultants
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We also developed our proprietary home loan reporting tool which provides amongst other things, 23 years Sibor history as well as 6 years worth of SOR.
Our service is free to you as banks pay us a commission on loan deals completed. Banks in turn save on staffing cost as we are not on their payroll. www.PropertyBuyer.com.sg/mortgagewww.SingaporeHomeLoan.netwww.iCompareLoan.com/consultant/