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How To Calculate Blended Interest Rates

Posted By Jim On 11/12/2008 @ 3:26 pm In Banking | 15 Comments

A blended interest rate is an interest rate over an amount where parts of that amount are charged, or earning, different interest rates. Blended interest rates are useful in making important comparisons between different offerings such as mortgages or high yield savings accounts [3].

With mortgages, the math is simple. You’re calculating the rate based on two separate sums. With a bank, it’s slightly more complicated because you are often accruing interest at one rate for part of the year and then accruing it at another rate for the rest of the year. We’ll explain both.

Mortgages

In the home mortgage example, let’s say you have the choice of getting one loan at $100,000 for 6.00% APY or two loans – one at $80,000 for 5.75% APY and one at $20,000 for 6.50% APY. Which is better? In order to make the comparison, you need to calculate the blended interest rate. Fortunately, it’s an easy calculation.

Take each amount and multiply it by the interest rate. Then add all those numbers together and divide by the total amount. In the above example, that would be:

($80,000 x 0.0575 + $20,000 x 0.065) / $100,000 = 0.0590

The blended rate is 5.9%. It is better to get the two loans.

Mortgages Blended Rate Calculator:
Of course I couldn’t leave you hanging without an easy way to calculate this (no commas or dollar signs please):

First Loan: Amount: , Interest Rate: %
Second Loan: Amount: , Interest Rate: %
Third Loan: Amount: , Interest Rate: %
The blended rate is: %

NOTE: You can also use the above calculator to figure out your blended rate of return on multiple investments with different interest rates, it’s the same equation whether you are earning or paying interest.

Bank Interest

Now we get to the example of one sum accruing interest at one rate for part of the year and at another rate for the rest of the year. This is common if your bank offers a promotional rate for new account holders. Everbank [4] is good example – they offer 4.01% APY for the first three months, then 3.21% APY thereafter.

The first step is determining the APR of both rates. Assuming a monthly period, the APR – APY Calculator [5]tells us that the rates are 3.93% APR and 3.16% APR. Dividing each by twelve, we learn that for the first three months your balance will increase by 0.3792% and then increase by 0.2942% thereafter. The blended rate is:

= ( (1+r1/tp)^r1p x (1+r2/tp)^r2p ) – 1
= ( (1.003275)^3 x (1.002633)^9 ) – 1
= ( 1.00985721200 x 1.0239481162 ) – 1
= ( 1.0340414 ) – 1
= 3.40% APY

Legend:

  • tp is the total number of periods, in our case it was 12,
  • r1 is the first period’s interest rate (APR),
  • r1p is the number of periods you get that promotional interest rate,
  • r2 is the second period’s interest rate (APR),
  • r2p is the number of periods you get that second interest rate (we limit it to 12 months to calculate APY).

To makes things simple, here’s a quick and dirty blended interest rate calculator.

First Period: Interest Rate: % Periods:
Second Period: Interest Rate: % Periods:
The blended rate is: %

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[3] high yield savings accounts: http://www.bargaineering.com/articles/top-5-online-banks-savings-or-checking-accounts.html

[4] Everbank: http://www.bargaineering.com/articles/r/everbank.php?tag=blendedRates

[5] APR – APY Calculator : http://www.bargaineering.com/articles/apr-apy-calculator.html

Thank you for reading!