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Present Value - Future Value Amortization Schedule

The effective interest rate, EIR, is a very useful and informative number. The EIR allows mortgages and loans to be compared before delving into points and transaction fees. If two loans or mortgages have the same EIR, they are equivalent and cost the borrower the same in interest. Using EIRs to compare loans or mortgages removes the uncertainty of not knowing the type of "compounding" used.

The following example using monthly compounding and 12% as the Annual Interest Rate was selected on purpose as 1% per month would be easier to visualize. Any other type of compounding could have been chosen. The PV/FV schedule is a powerful tool that can be used to explain a few important concepts.

If you borrowed $10,000 for one year at an annual interest rate of 12% and were given an amortization schedule it would appear as shown below;

(Screenshot 1)

You might be tempted to conclude that the lender made only $661.85 in interest for the year. You would be correct if the lender took your monthly payments and put them under a mattress. However the lender reinvests your monthly payments each month (deemed reinvestment) and ends up with more interest due to the compounding effect.

The effective interest rate (EIR) for this loan is 12.68250% because of monthly compounding. Take the EIR as a decimal and add 1 to it and you have

1.0 + 0.126825 = 1.126825

$10,000 x 1.126825 = $11,268.25

In essence the lender gets back his $10,000 at the end of the year plus $1,268.25 in interest due to reinvestment. The EIR is a very informative number because by adding 1 to it and multiplying by the original you discover the lenders actual return on investment.

As further proof of this make all the payments zero in the amortization schedule and you discover that the accumulation is the same $11,268.25 after 12 payments.

(Screenshot 2)

If you fancy yourself as a mathematician you will be interested to note that any financial calculator (as shown below) will arrive at the same numbers.

Notice that if the Number of Periods of the loan is chosen as a year (or a multiple of a year) the financial calculator will always calculate the effective interest rate 12.6825%

(Screenshot 3)

and if the Number of Periods is entered as one month, the Interest Rate per Period is 1%

(Screenshot 4)

 

ANOTHER EXAMPLE
When mortgage or loan payments are set to zero this type of amortization schedule using the MORTGAGE2 PRO software, displays what the cash outlay will accumulate to after a given amount of time. The MORTGAGE2 PRO software program allows users to set the amortization schedule payments to zero, after the schedule has been generated. One simply changes the first payment in the schedule to zero and then copies it automatically to the end of the schedule.

A simple financial plan to follow in order to retire is as follows. Once your mortgage is paid off use the weekly payments to invest in a financial vehicle that will give you at least the same return your lender was receiving on your mortgage.

Assume a young married couple age 20 ,took out a $150,000 mortgage in 1984 and paid it off in 20 years, when they were 40 years old. They have been accustomed to the weekly outlay of $247.19 so why not continue putting $247.19 away each week for the next 20 years in a financial vehicle for retirement. Consult a Financial Planner to explain the details of how to do it properly, so that the payments are tax deductible.

(Screenshot 5)

The mathematics of the plan are as follows. The negative amortization schedule below is actually showing what $247.19 per week will accumulate to after 20 years.

(Screenshot 6)

After 20 years, the 60 year old couple will have a retirement nest egg of almost half a million dollars ($494,905.02). More than likely the interest rate will not be exactly 6% for the next 20 years; however 6% is a conservative estimate of what to expect. It is a starting point that can be refined. The point is, ... you need a first approximation or starting point, .. rather than doing nothing, guessing, or assuming you will win the lottery.

As a side issue on weekly or biweekly payment mortgages, check out how the same example can exhibit two different effective interest rates (EIR) depending upon how your lender chooses the number of days in the year.

 

 


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