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?
1.025^2 ==1.050625 - 1 x 100 ==5.0625% comp. semi-annually. But 5% is compounded annually!!.
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.
