home loans with different rests: computing their effective rates

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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







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.







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.







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.







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







Furthermore, we have

PVF= principalinstalment







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







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.







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%.







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.







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







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







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







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.







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







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







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.







Table 4

ENR )%(9.78 Daily Rest

10.00 Monthly Rest

10.21 Annual Rest







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







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.







Table 6: Effective Interest Rate (%)

Effective Interest Rate%( )

10.23 Daily Rest

10.47 Monthly Rest

10.70 Annual Rest







About Property Buyer Mortgage Consultants

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We also help property buyers in their buying process helping them avoid pitfalls from unscrupulous property agents. (We are not property agents, therefore there is no conflict of interests.)

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/




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home loans with different rests: computing their effective rates

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