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amortization.com
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When two loans are blended or consolidated into one loan interesting questions arise!
The example shown is a loan of $200,000 at 3% and a second loan of $50,000 at 6%. This example could be considered a first and second mortgage even though the amortization period for a second mortgages is usually shorter. The same example could also be viewed as a mortgage with 5 years remaining in the term and wanting to borrow an additional $50,000 at 6% in order to do home renovations. The same amortization period is chosen to keep the example simple. Monthly compounding was selected because that type of compounding is applicable for personal loans and collateral mortgages in Canada and all variations of loans and mortgages in the USA. The logic and calculations are identical had semi-annual compounding been selected.

What is the blended interest rate for the new blended loan? The answer depends upon your point of view. From the borrowers point of view, adding the two separate monthly payments together and paying down the total of the two principals over the next 5years is the obvious route. From a lenders point of view, the lender would like to receive the same yield (return on investment as per deemed reinvestment) as the sum of the yields for the two separate loans. Will this new blended rate satisfy both the lender and the borrowers concerns?

Probably the first and obvious answer one would jump at is the arithmetic average rate of 4.5% (that is (3+6)/2=4.5% ). Probably the next answer would be the weighted average of 3.60% (that is 200/250 x .03 + 50/250x.06 = 3.60%)

The actual blended interest rate that would satisfy the lender and the borrowers concerns is arrived at as follows.

Negative amortization schedules (a PV/FV in a grid format) for the two separate loans demonstrate what the monthly cash flows would accumulate to over 60 months. Add the two accumulations together ( $232,323.36 + $67,442.52) and you arrive at the future value. It is assumed that the lender reinvests, at the same interest rate, your monthly payments as he receives them (aka deemed reinvestment). Using a present value of $250,000 and a period of 5 years the effective interest rate (the actual interest rate per period) is calculated as 3.697536% which corresponds to an annual interest rate of 3.64% at two decimal places( because of “monthly compounding”).

In this example, if the lender offered you the weighted average of 3.60% you would save yourself an extra few dollars in interest costs (approx $269) over the next five years, compared to having two separate loans at their respective rates of 3% and 6%.

Note it is very difficult if not impossible to get present value future value numbers to agree to the penny in these FV/PV calculations because the exponent function in the mathematical equation is very sensitive to the number of decimal places used for describing the annual interest rate, that is why the total of the two monthly payments do not agree.

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