Bank A pays 4.79% compounded monthly, while Bank B pays 4.8% compounded quarterly.
Which bank pays more?
value of $1.00 at end of 1 year:
Bank A : amount = (1 +.0479/12)^12 = ...
Bank B : amount = (1 + .048/4)^4 = ..
compare the results
bank a
To determine which bank pays more, we need to compare the effective annual interest rate (APY) of both banks.
For Bank A:
The nominal (stated) interest rate is 4.79% and it is compounded monthly.
To calculate the effective annual interest rate (APY) for Bank A, we can use the formula:
APY = (1 + (nominal interest rate / number of compounding periods)) ^ number of compounding periods - 1
In this case, the number of compounding periods is 12 (monthly compounding).
So, for Bank A:
APY = (1 + (4.79% / 12))^12 - 1
= (1 + 0.03992)^12 - 1
≈ 0.0499 or 4.99%
For Bank B:
The nominal (stated) interest rate is 4.8% and it is compounded quarterly.
To calculate the effective annual interest rate (APY) for Bank B, we can use the same formula as above, but with different values:
APY = (1 + (nominal interest rate / number of compounding periods)) ^ number of compounding periods - 1
In this case, the number of compounding periods is 4 (quarterly compounding).
So, for Bank B:
APY = (1 + (4.8% / 4))^4 - 1
= (1 + 0.012)^4 - 1
≈ 0.0488 or 4.88%
Comparing the two APYs, we can conclude that Bank A pays more, as its APY of 4.99% is higher than Bank B's APY of 4.88%. Therefore, Bank A pays more.