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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-> 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 1190790: 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? Answer by Theo(13342) (Show Source):
You can put this solution on YOUR website! 4% nominal annual rate, compounded semi-annually, gives you an effective annual rate of 4.04%.
5% nominal annual rate, compounded monthly, gives you an effective annual ratel of 5.116189788%.
these numbers are derived as follows:
4% / 100 = annual interest rate of .04.
divide that by 2 to get semi-annual interest rate of .04/2 = .02.
add 1 to that to get semi-annual growth rate of 1.02.
raise that to the power of 2 to get annual growth rate of 1.02 ^ 2 = 1.0404.
subtract 1 from that to get effective annual interest rate of .0404.
multiply that by 100 to get effective annual interest rate of 4.04%.
5% / 100 = annual interest rate of .05
divide that by 12 to get monthly interest rate of .00416666667.
add 1 to that to get monthly growth rate of 1.00416666667.
raise that to the power of 12 to get annual growth rate of 1.00416666667 ^ 12 = 1.051161898.
subtract 1 from that to get effective annual interest rate of .051161898.
multiply that by 100 to get effective annual interest rate of 5.1161898%.
all numbers shown are rounded to the amount of decimal places that can be displayed on your calculator.
the actual numbers stored in the calculator are rounded to more than that.
for example, your calculator might show the number rounded to 7 or 8 decimal digits.
the actual number stored is rounded to more like 15 or 16 decimal digits.
your nominal interest rate of 4% becomes an effective annual interest rate of 4.04%, when compounded semi-annually.
your nominal interest rate of 5% becomes an effective annual interest rate of 5.1161898%, when compounded monthly.
you would prefer the bank that gives you 5% compounded monthly, because your investment earns you more each year.
the following graph shows you how much 1000 dollars earns you when invested at the 4% compounded semi-annually versus the 5% compounded monthly.
