SOLUTION: One bank quotes interest at 4% p.a. compounded semi annually. Another bank offers interest of 5% compounded monthly. Which one of these banks would you prefer and why?

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Question 1191432: One bank quotes interest at 4% p.a. compounded semi annually. Another bank offers interest of 5% compounded monthly. Which one of these banks would you prefer and why?
Found 4 solutions by Alan3354, MathTherapy, math_tutor2020, ikleyn:
Answer by Alan3354(69443) About Me  (Show Source):
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One bank quotes interest at 4% p.a. compounded semi annually. Another bank offers interest of 5% compounded monthly. Which one of these banks would you prefer and why?
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A higher rate compounded more often would generate more interest.
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I prefer the bank with the hottest girl teller.

Answer by MathTherapy(10552) About Me  (Show Source):
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One bank quotes interest at 4% p.a. compounded semi annually. Another bank offers interest of 5% compounded monthly. Which one of these banks would you prefer and why?
That's so TRUE, @ALAN. Me too!!

Answer by math_tutor2020(3817) About Me  (Show Source):
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The compound interest formula is
A = P*(1+r/n)^(n*t)

Let's say we have P = 100 dollars to deposit and we do so over t = 1 year.

The first scenario has r = 0.04 and n = 2
A = P*(1+r/n)^(n*t)
A = 100*(1+0.04/2)^(2*1)
A = 104.04

The second scenario involves r = 0.05 and r = 12
A = P*(1+r/n)^(n*t)
A = 100*(1+0.05/12)^(12*1)
A = 105.116189788173
A = 105.12

The second scenario is better.

Answer by ikleyn(52786) About Me  (Show Source):
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.

To answer this question, calculations are not necessary.

The second bank has higher nominal annual percent rate and makes compounding more often.

These are two reasons/(two factors) what both work in the same direction, providing more high actual percentage rate
of the second bank comparing to the first bank.