Bark A citers a one-year $C D$ at a rate of $7.4 \%$ compounded semiannually. Bank B offers a one-year CD at a rate of $7.3 \%$ compounded daily. Compute the annual percentage yield for each CD and determine which offer the bether deal.

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Grade 7

Calculate unit rates with fractions

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Q. Bark A citers a one-year

C D

at a rate of

7.4 \%

compounded semiannually. Bank B offers a one-year CD at a rate of

7.3 \%

compounded daily. Compute the annual percentage yield for each CD and determine which offer the bether deal.

Calculate APY for Bank A: For Bank A, we need to calculate the APY for a $7.4\%$ interest rate compounded semiannually. $\newline$ APY = $(1 + \frac{r}{n})^{n*t} - 1$ , where $r$ is the annual interest rate, $n$ is the number of times interest is compounded per year, and $t$ is the time in years.
Calculate APY for Bank A: Plug in the values for Bank A: $r = \frac{7.4}{100} = 0.074$ , $n = 2$ (since it's semiannual), and $t = 1$ (since it's for one year). $\newline$ APY for Bank A = $(1 + \frac{0.074}{2})^{(2\cdot1)} - 1$ .
Calculate APY for Bank A: Calculate the APY for Bank A: $(1 + 0.037)^2 - 1$ . $\newline$ APY for Bank A = $(1.037)^2 - 1$ .
Calculate APY for Bank A: APY for Bank A = $1.076369 - 1$ . APY for Bank A = $0.076369$ or $7.6369\%$ .
Calculate APY for Bank B: For Bank B, we need to calculate the APY for a $7.3\%$ interest rate compounded daily. $\newline$ APY $= (1 + \frac{r}{n})^{n*t} - 1$ , where $r$ is the annual interest rate, $n$ is the number of times interest is compounded per year, and $t$ is the time in years.
Calculate APY for Bank B: Plug in the values for Bank B: $r = \frac{7.3}{100} = 0.073$ , $n = 365$ (since it's daily), and $t = 1$ (since it's for one year). $\newline$ APY for Bank B = $(1 + \frac{0.073}{365})^{365 \times 1} - 1$ .
Calculate APY for Bank B: Calculate the APY for Bank B: $(1 + 0.0002)^{365} - 1$ . $\newline$ APY for Bank B = $(1.0002)^{365} - 1$ .
Calculate APY for Bank B: APY for Bank B = $1.075646 - 1$ . APY for Bank B = $0.075646$ or $7.5646\%$ .
Compare APYs: Compare the APYs of both banks to determine the better deal. Bank A's APY is $7.6369\%$ and Bank B's APY is $7.5646\%$ .
Bank A is better: Bank A offers a higher APY, so Bank A is the better deal.