Suppose you deposit $3,000 in a bank that pays 5 percent interest compounded twice a year. The actual annual interest rate you receive is

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Quizplus · Accepted Answer

The actual annual interest rate, considering semi-annual compounding, is calculated using the formula for compound interest: $A = P(1 + \frac{r}{n})^{nt}$, where $A$ is the amount of money accumulated after n years, including interest, $P$ is the principal amount (initial investment), $r$ is the annual interest rate (decimal), $n$ is the number of times that interest is compounded per year, and $t$ is the time the money is invested for in years. For a 5 percent interest rate compounded twice a year, the effective annual rate (EAR) can be calculated as $EAR = (1 + \frac{0.05}{2})^{2} - 1 = 1.025^2 - 1 = 1.050625 - 1 = 0.050625$, or 5.0625 percent, which rounds to approximately 5.06 percent.

Suppose You Deposit $3,000 in a Bank That Pays 5