Home Loans How To Compute The Effective And Nominal Interest Rates

Home Loans: How To Compute The Effective And Nominal Interest Rates?

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Interest rate is the cost of borrowing

But the interest rate stated in our credit cards or loans applications may not be the true cost.

Why?

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The rate given is the per annum (p.a.) rate.

For example, in a home loan letter of offer you may find a line that says, “First year interest rate is 1% p.a.”.

But since the base period for interest calculation can be more than once a year,

So there can be a difference in interest cost for loans with the same interest rate per annum, loan amount and duration.








The frequency in which the outstanding loan amount is calculated, is known as rest. Most Singapore home loans follow a monthly rest, while a few is on daily- and annual-rest basis.

All else being equal (including the frequency of installments)

A shorter rest will reduce interest payment.







Thus an effective annual interest rate is needed to measure the true borrowing cost.

The interest rate per annum is only the nominal interest rate.

This nominal rate is equal to the effective rate when a loan is on annual-rest basis and installments are also made annually.







How to obtain the annual effective rate and nominal rate?






What is the math formula for the annual effective rate?

The annual effective interest rate, re, is actually the ratio of the amount of interest earned during a year to the amount of principal outstanding at the beginning of the year. The above equation, Eq 1, shows the relation between the effective rate and nominal rate.

r e :effective ratern :nominal rate

m :number of compounding per year





So, if you take a monthly-rest loan with an interest rate of 5% p.a., to find the annual effective rate you first definern = 5% = 0.05m = 12 An important point to note is that the effective rate is always larger than the nominal if compounding is done more than once a year, m > 1. For a daily compounding loan, the m = 365







Table 1 presents the effective rate across the three different rests:

Effective rate)%( Type of loan

5.13 Daily-rest with daily installments 5.12 Monthly-rest with monthly installments

5.00 Annual-rest with annual installments







The effective interest is lower for shorter rest loans only if the frequency of installments are the same, and all else are equal.

For example, comparing a daily-rest loan with monthly installments and a monthly-rest loan with monthly installments, the former will have a lower effective rate.







What is the math formula for the annual nominal rate?

Conversely, if you have the effective rate, but wish to find the nominal. You can use the below formula:

Using the same example, and inserting the values into Eq 2: we obtain the nominal rate of 5%, as expected.

rn=m [(1+ re)1m−1]







What are the Excel functions?let Excel do the calculation for you

Table 2: Math Formulas and Excel Functions

Excel Function Math Formula =EFFECT (nominal_rate, npery)

=NOMINAL (effect_rate, npery)

npery is equivalent to m, or the number of compounding per year

r e=(1+r nm

)m

−1

rn=m [(1+ re)1m−1]







But before you can utilize these two Excel functions, you need to include an add-on – the Excel Analysis ToolPak.

To do so in Excel 2007, you have to click on the Office button on the top left- hand corner as in Figure 1







Figure01







Figure02







Figure03







Figure04







Now you are all set to use the EFFECT and NOMINAL functions







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/mortgagewww.SingaporeHomeLoan.netwww.iCompareLoan.com/consultant/




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Home Loans How To Compute The Effective And Nominal Interest Rates

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