Home Loans With Different Rests: Computing Their Effective Rates

• 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
PresentValueFactor(PVF)=(1− (1+
rn
(m)
m
)
− my
)÷
rn
(m)
m
rn
(m)
:nominal rateorthe ENR
m:number of compounding per year
y:numberof years

Furthermore, we have
PVF=
principal
instalment

Finding ENR using Excel
Excel 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
periods
PMT: (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
ExplanationValue
Payments are due at the end of the period. (default)0
Payments 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 Repayments
Number of Payment Periods = 12 * 20 = 240
Monthly Installment for the First Year = $ 9,788.30

Using RATE
Loan B
Annual Rest with Monthly Repayments
Number of Payment Periods = 12 * 20 = 240
Monthly 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

Table 2: Monthly Installment for the First Year
The monthly payment amount for the three rests
Monthly Payment ($)
9,506.0Daily Rest
9,650.2Monthly Rest
9,788.3Annual Rest

Enter the below syntax to find the ENR,
Table 3
Syntax
=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 (%)
9.78Daily Rest
10.00Monthly Rest
10.21Annual 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 (%)
10.23Daily Rest
10.47Monthly Rest
10.70Annual Rest

About Property Buyer Mortgage Consultants
Property Buyer Mortgage Consultants is a research focused independent mortgage broker. We
emphasize a consultative approach where we match our client’s financial situation with the best
fit mortgage loan, not simply a cheap loan.
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/mortgage
www.SingaporeHomeLoan.net
www.iCompareLoan.com/consultant/

Home Loans With Different Rests: Computing Their Effective Rates

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Home Loans With Different Rests: Computing Their Effective Rates