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Dr. Zaius invests $10,000 in a CD with an annual interest rate of 4% that compounds semi-annually (twice a year). After six months, he rolls over the CD into another CD with an annual interest rate of 5% that compounds annually. After six months in the second CD, how much does Dr. Zaius have, in dollars?

 Jan 9, 2022
 #1
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10 000 * 1.02   * 1.025= $ ........

 Jan 9, 2022
 #3
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1.025^2 ==1.050625 - 1 x  100 ==5.0625% comp. semi-annually. But 5% is compounded annually!!.

Guest Jan 9, 2022
 #4
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At the end of the first year you would have   1.05   half a year is half of that @ 1.025 ....you get no benefit from compounding unless you have it for more than a year.....because it is ANNUAL compounding.

Guest Jan 9, 2022
 #5
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  I think you still have to use the compounding interest calculation   (1 + r/n)nt      which will result in interest of 2.4695 %  for the six months that it is in the annual compound  account 

      resulting in    10,000 x 1.02   x 1.1024695    for the final $ amount

Guest Jan 9, 2022
 #2
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FV ==10,000  x  1.02 ==$10,200 - value of his 10,000 for the first 6 months.

 

Convert  5% interest rate from comp.annually to equivalent rate comp. semi- annually.

 

1.05^(1/2) ==sqrt(1.05) ==1.0246950

 

$10,200  x  1.0246950 ==$10,451.89 - value of his $10,000 after the 2nd 6-month period.

Note: Both calculations are based on compounding the interest rate every 6 months.

 Jan 9, 2022

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