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Home Loan | Commercial Loan | Refinance Loan | *Financial Planning
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How To Determine the Effective Interest on Home Loans With Different Rests
As discussed in the previous article, the nominal interest rate on your housing loan is different from
the effective interest rate. The nominal rate is typically the interest rate per annum indicated on the
documents, while the effective rate is the actual, accurate amount calculated against each
compounding period specific to your loan. The effective interest is the cost of the loan, which you
will have to pay on top of the amount you borrowed.
Having different reference rates, lending companies may not always be up front about the effective
interest when discussing the loan with their clients. Because of the inconvenience this may cause
loan-takers, a law has been enforced as of June 1, 2012, requiring all accredited moneylenders in
Singapore to specify the effective interest rate for every loan. To learn more about this, you can
proceed to the Ministry of Law website and read the article with the heading, "Amendments to the
Moneylenders Rules to take effect from 1 June 2012". You may also visit the site of the Insolvency
& Public Trustee's Office, and go through the section on "What Borrowers Should Know About
Effective Interest Rates".
Singapore banks, however, are not legally required to indicate the effective interest rates for credit
facilities. Thus, it could be rather perplexing for loan-takers since the actual payable amounts are
not revealed directly.
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Fortunately, there is a way for you to calculate the effective interest for your housing loan. Below is
a brief guide showing you how to compute the effective interest for loans with different rests. To
simplify this tutorial, we will assume that the mortgages are paid in monthly installments.
The Equivalent Nominal Rate
One of the things you need to know early on is the Equivalent Nominal Rate or ENR per annum.
The ENR will help you make a balanced evaluation between housing loans that have different rests
but the same number of installments frequency.
In finding the ENR, you must first determine the Present Value Factor, or PVF of the annuity.
Represented in equation form, it is:
(m) −my
(m)
rn
rn
Present Value Factor ( PVF )=(1−(1+
) )÷
m
m
(m)
r n : nominal rate or the ENR
m: number of compounding per year
y : number of years
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Alternately, you may also refer to the following equation:
PVF=
principal
instalment
The ENR is calculated by multiplying the RATE (to be explained below) by the number of
compounding periods in a year. Given that the number of compounding periods is represented as m,
ENR = m*RATE
It's possible to calculate the ENR manually, though this often takes time. Luckily, there's a faster
and easier way to do it using a financial calculator, or a spreadsheet software.
Not everyone has a financial calculator, though most people today have access to a computer. For
this reason, the following tutorial shows you how to compute for the values using a spreadsheet
application like Microsoft Excel.
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The RATE Function
Your spreadsheet program is equipped with a RATE function, which can help you determine the
ENR. RATE gives you the nominal interest rate per period of an annuity, or
r n(m)
m
.
The syntax for this is RATE (NPer, PMT, PV, FV, Type, Guess)
In which …
- NPer: the total number of payment periods in an annuity.
- PMT: the total payment due for a particular compounding period, which is typically the principal
amount plus the interest.
- PV: Present Value, or the current total amount of the loan.
- FV: Future Value, or the amount you should be left with after all payments have been made. If this
variable is not included, the Excel will assume that it is 0 by default.
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- Type: The time when payment is due. It can be represented by either 1 or a 0. A 1 indicates that
payments must be made at the beginning of the period, while a 0 indicates that payment is due. If
this variable is not included, Excel assumes that it is of 0.
- Guess: Your estimate of what the RATE is. If this is omitted, it will be assumed to be 10%.
It's important to remember that RATE does not depend on the loan amount and installment per
payment period. RATE will be the same for loans with the same number of payment periods and
nominal interest rate per annum.
To help you get a better grasp, take a look at the following two sample loans:
SAMPLE LOAN A
Loan Quantum: S$ 1,000,000
Tenure: 20 years
Interest Rate: 10%, p.a.
Rest: Annual
Payment: Monthly installments
Total Number of Payment Periods (for the entire tenure): 12 x 20 = 240
Monthly Instalment for the First Year: S$ 9,788.30
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SAMPLE LOAN B
Tenure: 20 years
Rest: Annual
Payments: Monthly installments
Total Number of Payment Periods: 12 x 20 = 240
Monthly Instalment for the First Year: S$ 48,941.51
On your spreadsheet, enter the following syntax:
Table 1
Syntax
Loan A
= RATE (240, 9788.3, -1000000)
Loan B
= RATE (240, 48941.51, -5000000)
For both loans, the RATE will come out as 0.85.
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To calculate for the ENR per annum, multiply the RATE with the number of compounding periods.
ENR = m*RATE
= 12*0.85
= 10.20
Computing for the ENR for Loans With Different Rests (with Monthly Installments)
For this section, we'll need to use hypothetical values that will help you understand the process. We
will refer once more to "SAMPLE LOAN A", which was provided earlier.
SAMPLE LOAN A
Tenure: 20 years
The following table allows you to compare the monthly payments for this loan against three
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different rests:
Table 2: Monthly Instalment for the First Year
Monthly Payment ($)
Daily Rest
9,506.0
Monthly Rest
9,650.2
Annual Rest
9,788.3
To find the ENR, enter the syntax provided below.
Table 3
Syntax
Daily Rest
=12* RATE (240, 9506.0, -1000000)
Monthly Rest
=12* RATE (240, 9650.2, -1000000)
Annual Rest
=12* RATE (240, 9788.3, -1000000)
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As a result, Excel will provide you with the following ENR, based on a monthly rest.
Table 4
ENR (%)
Daily Rest
9.78
Monthly Rest
10.00
Annual Rest
10.21
This can help you translate the interest into a more comprehensible form, so you can make a better
comparison between loans with different rests.
Going even further, you may like to calculate the effective interest rate per annum as well. Now,
input the following syntax on your Excel spreadsheet:
Table 5
Syntax
Daily Rest
= EFFECT (9.78%, 12)
Monthly Rest
= EFFECT (10%, 12)
Annual Rest
= EFFECT (10.21%, 12)
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This ultimately gives you a better way to determine and assess the actual cost of your housing loan.
Naturally, a shorter rest means more compounding periods, and lower effective interest. Thus, a
loan with a daily rest has a lower effective interest compared to loans with a monthly or annual rest,
all else equal including the frequency of instalments.
Table 6
Effective Interest Rate (%)
Daily Rest
10.23
Monthly Rest
10.47
Annual Rest
10.70
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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
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