SOLUTION: You have searched online and found banks offering two different interest rates for the same service: Bank A offers 4.5%/a and Bank B offers 4.9%/a. All other terms of the service a

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Question 1202728: You have searched online and found banks offering two different interest rates for the same service: Bank A offers 4.5%/a and Bank B offers 4.9%/a. All other terms of the service are the same.
In what situation would you be better off choosing Bank B? Explain
Found 2 solutions by ikleyn, math_tutor2020:
Answer by ikleyn(52781) About Me  (Show Source):
You can put this solution on YOUR website!
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What do YOU think ?

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Answer by math_tutor2020(3817) About Me  (Show Source):
You can put this solution on YOUR website!

It should be fairly clear that bank B is the better offer since 4.9% > 4.5%

You can think of it like saying 49 > 45.

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Let's look at a slightly more complicated example.

Bank A offers 6.25% compounded daily.
Bank B offers 6.30% compounded semi-annually.
Which bank is the better deal?

The annual percentage yield (APY) formula is
APY = (1 + APR/n)^n - 1

For bank A,
APY = (1 + APR/n)^n - 1
APY = (1 + 0.0625/365)^365 - 1
APY = 0.06448876344422
APY = 0.06449
APY = 6.449%

And bank B,
APY = (1 + APR/n)^n - 1
APY = (1 + 0.063/2)^2 - 1
APY = 0.06399225
APY = 0.06399
APY = 6.399%

Bank A offers the better APY even though 6.25% < 6.30%
Bank A gets a bigger boost because the interest is compounded far more frequently.

This entire section is a hypothetical example of course.