home loans with different rests creating their amortization schedule

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Home Loans With Different Rests: Creating Their Amortization Schedule

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Explaining About The Set-up Of The Amortization Schedule For

Mortgages With Different Rests







Rest (the compounding period)

It is the frequency in which the outstanding loan amount is calculated

The more frequently the loan is calculated the lower the interest payments will be, all else being equal.







Each time repayment is made the outstanding loan amount is reduced and so will the interest chargeable if the loan is re-calculated.

If a loan on an annual-rest basis is repaid monthly the interest for the entire year will still remain the same the financier uses the outstanding loan at the beginning of the year for interest computation.

Because

Because







Most Singapore home loans follow a monthly rest, while a few is on daily-

and annual-rest basis.








Example

Using the below loan details, we will proceed to create the amortization schedule for daily-, monthly- and annual-reducing loans.

Loan Quantum = S$1 millionLoan Tenure = 20 years

Interest Rate = 10% p.a. The Excel template workbook with pre-set formulas used throughout

this article can be downloaded here.



http://www.icompareloan.com/resources/wp-content/uploads/2013/04/Home-Loans-With-Different-Rests-Creating-Their-Amortisation-Schedule3.xlsx





Daily-rest loan with monthly installment

There are two main advantages of a mortgage that are calculated daily.

Firstly the total interest payable will be relatively lower.

Secondly, if partial repayment is made, the interest that will be charged is reduced by the next day since the outstanding principle is calculated everyday.







How do we create the amortization schedule?

With the aforementioned loan, we need to find the number of compounding periods for the entire loan duration as well as the

daily interest rate







For simplicity, we assume that every year in the loan has 365 days.

Total Periods = 365 x 20 = 7,300

Next, we calculate the daily interest rate.

Daily Interest Rate = 10% / 365 days = 0.0274% (approximately)

In the Excel sheet, we enter these loan details.







After entering the loan details, the payment, principal, interest and balance, the first period will appear in the Excel sheet with the pre-entered formulas, as seen in the next figure.






Select D12:G12 then drag and pull to the 7,300th period





However, the repayments are monthly so we need to find the total amount for 30 days

(We assume here that there are 30 days in each month).

Using the pre-set formula in the Excel sheet and dragging it

down, we get the next result:







Monthly-rest with monthly installment

Similar to the daily-reducing loan, we find the total periods and monthly interest, which are

Total Periods = 12 x 20 = 240

Monthly Interest = 10%/ 12 months = 0.083% (approximately)In the Excel sheet, we get as next:







Repeat the steps for the daily-rest loan to obtain the amortization schedule and you will obtain something like the next:






Repeat the steps for the daily-rest loan to obtain the amortization schedule





Annual-rest with monthly installment

Finally we have the annual-reducing loan.

Since the frequency of loan calculation is the same as the loan quantum. We have

Total Periods = 20

The annual interest rate is also already given. Hence we have the following:







The amortization schedule will be like the next:







But repayment is made monthly. So we must divide all the yearly figures by 12.

For example in the first year:

Total Monthly Payment ($) = 117,459.62 / 12 = 9,788.30 Total Monthly Principal ($) = 17,459.62 / 12 = 1,454.97 Total Monthly Interest ($) = 100,000.00 / 12 = 8,333.33

In the Excel sheet, it will be like this:







Conclusion

For simplicity's sake, throughout this section, we assume that each month has 30 days and so for the monthly outlay for the daily-reducing loan, we simply sum up the figures for 30 days.







Now, we compare the monthly payment, principal and interest across the three types of rests.

We only use the first month's amortization schedule.

From Table 1, we see that the total payment and interest is the least for the daily-reducing loan.

Example







Table 1: Comparison of Amorisation Schedule for the 1st Month

Monthly Payment ($)

Monthly Principal ($)

Monthly Interest ($)

9,506.0 1,292.0 8,214.1 Daily Rest

9,650.2 1,316.9 8,333.3 Monthly Rest

9,788.3 1,455.0 8,333.3 Annual Rest







In Table 2, we clearly see the difference in interest payment for the first year.

As expected the interest is always lower for the daily-rest loan, followed by monthly, and finally annual.






Table 2: Comparison of Monthly Interest Payment ($) for the 1st Year

Annual Rest Monthly Rest Daily Rest8,333.3 8,333.3 8,214.1 1st Month8,333.3 8,322.4 8,203.4 2nd Month8,333.3 8,311.3 8,192.6 3rd Month8,333.3 8,300.1 8,181.8 4th Month8,333.3 8,288.9 8,170.9 5th Month8,333.3 8,277.5 8,159.9 6th Month8,333.3 8,266.1 8,148.8 7th Month8,333.3 8,254.6 8,137.6 8th Month8,333.3 8,242.9 8,126.3 9th Month8,333.3 8,231.2 8,114.9 10th Month8,333.3 8,219.4 8,103.4 11th Month8,333.3 8,207.5 8,091.8 12th Month





If that isn't enough, we note that the total interest payable for the entire loan duration is lowest for the daily-rest loan.







Table 3: Comparison of Total Interest Payments

Total Interest ($)

1,313,134.5 Daily Rest

1,316,051.9 Monthly Rest

1,349,192.5 Annual Rest







With the daily-rest, you can reap interest-saving of $(1,316,051.9 – 1,313,134.5) = $2,917.40 as compared to the

monthly-rest.

When comparing the monthly-rest with the annual-rest

The interest-saving is even greater at $(1,349,192.5 – 1,316,051.9) = $3,3140.6.







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