SOLUTION: Determine the effective annual yield for each investment. Then select the better investment. Assume 360 days in a year.
5% compounded semiannually; 4.9% compounded daily
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Question 1175042: Determine the effective annual yield for each investment. Then select the better investment. Assume 360 days in a year.
5% compounded semiannually; 4.9% compounded daily
The effective annual yield for a 5% compounded semiannually investment is %.
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
5% per year compounded semi-annually is equal to 5% / 100 = .05 per year divided by 2 compounding periods per year = .025 per semi-annual period.
add 1 to that to get a growth factor of 1.025 per semi-annual time period.
raise that to the number of compounding periods per year to get 1.025 ^ 2 = 1.050625 - 1 = .050625 * 100 = an effective rate of 5.0625% per year.
4.9% compounded daily is equal to 4.9% / 100 = .049 per year divided by 360 compounding periods per year = .0001361111111 per daily time period.
add 1 to that to get a growth factor of 1.000136111 per daily time period.
raise that to the number of compounding periods per year to get 1.000136111 ^ 360 = 1.050216849 - 1 = .0502168489 * 100 = an effective rate of 5.021684887% per year.
5% compounded semi-annually give you an effective rate of 5.0625% per year.
4.9% compounded daily gives you an effective rate of 5.021684887% per year.
the 5% compounded semi-annually is a better investment than the 4.9% compounded daily because the effective rate per year is higher.
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