How To Calculate Blended Interest Rates
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.
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):
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 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 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.
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Tags: Calculators, Interest Rates, Mortgages
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It is the same thing as a weighted average. I keep track of a blended rate for all of my combined debts, from the highest-interest store credit card to my wife’s student loan, just as a way to get a sense of where I am.
The first scenario is the same as a weighted average (some call it blended), but the second one isn’t because of how the compounding works.
I might be missing something but I just did a test of the blended bank interest calculator and put in 5% at 3 months and 5% at 9 months and it gave me a blended rate of 5.12%. Is it just an anomaly that the rate comes out different if you put the same percentage in twice or is it an APR vs APY thing?
@Jessica: Yep, the calculators asks for APR as inputs and spits out APY. If you put 5% APR into the APR to APY calculator, the APY that it produces is 5.12%.
You scared me for a second!
Great stuff Jim. Just wondering if there is a place on your site that has all of your “calculators” in one place? I find them useful now, but would be even more useful for future reference and would like to come back and easily find them.
Thanks!
The easiest way would be to use the Calculator’s Tag page, it’ll list every post I’ve tagged with Calculator; that should do it for you.
Jim-
I have a question. I have a loan (loan A) of $7300 at an interest rate of 8.25% and another 16,800 (loan B) at an interest rate of 5.25%. My immediate thought was to pay off loan A, and not B because of the higher interest rate. But then I started thinking and started looking for calculators which would let me do some calculations but couldn’t see anything direct.
Can you help me? I am assuming it will also help others who are in the same situation!
Thanks much!
@Sam: Your immediate thought is correct, you want to pay off the higher interest rate loan in most cases. The only exceptions are if the interest is tax deductible, but with a 3% spread, it’s unlikely the 8.25% will have an effective interest rate lower than the 5.25%. Pay off the 8.25% first.
Jim-
Yes. The interest on loan A is tax deductible (part of mortgage) and loan B (car) is not. I did some calculations and it looks like the interest on loan A is only about $50 a month, which is pretty low I guess considering the interest rate….
@Sam: Using rough math, if the 8.25% interest is tax deductible and you’re in the 25% bracket, in theory you only pay the other 75% (because you deduct it and your taxes are reduced). 75% of 8.25% is 6.1875%, which is still higher than your 5.25% - so you’ll want to pay the second mortgage down.