Bark. A offers 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 offers the better deal. $\newline$ $A=P\left(1+\left(\frac{A P R}{n}\right)\right)^{n y}$

View step-by-step help

Home

Math Problems

Calculus

Find equations of tangent lines using limits

Full solution

Q. Bark. A offers 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 offers the better deal.

\newline

A=P\left(1+\left(\frac{A P R}{n}\right)\right)^{n y}

Calculate APY for Bank A: question_prompt: Calculate the annual percentage yield ( $APY$ ) for each $CD$ and determine which bank offers the better deal.
Calculate APY for Bank B: For Bank A, we need to use the formula for compound interest to find the APY. The formula is $A=P(1+(r/n))^{(nt)}$ , where $P$ is the principal, $r$ is the annual interest rate, $n$ is the number of times the interest is compounded per year, and $t$ is the time in years.
Compare APYs for better deal: Bank A's interest rate is $7.4\%$ or $0.074$ as a decimal. It's compounded semiannually, so $n=2$ . Since it's a one-year CD, $t=1$ .
Compare APYs for better deal: Bank A's interest rate is $7.4\%$ or $0.074$ as a decimal. It's compounded semiannually, so $n=2$ . Since it's a one-year CD, $t=1$ . Plug the values into the formula for Bank A: $A=P(1+(0.074/2))^{(2*1)}$ .
Compare APYs for better deal: Bank A's interest rate is $7.4\%$ or $0.074$ as a decimal. It's compounded semiannually, so $n=2$ . Since it's a one-year CD, $t=1$ . Plug the values into the formula for Bank A: $A=P(1+(0.074/2))^{(2*1)}$ . Calculate the expression inside the parentheses for Bank A: $1+(0.074/2) = 1+0.037 = 1.037$ .
Compare APYs for better deal: Bank A's interest rate is $7.4\%$ or $0.074$ as a decimal. It's compounded semiannually, so $n=2$ . Since it's a one-year CD, $t=1$ . Plug the values into the formula for Bank A: $A=P(1+(0.074/2))^{(2*1)}$ . Calculate the expression inside the parentheses for Bank A: $1+(0.074/2) = 1+0.037 = 1.037$ . Now raise this to the power of $2$ for Bank A: $(1.037)^2 = 1.0757$ approximately.
Compare APYs for better deal: Bank A's interest rate is $7.4\%$ or $0.074$ as a decimal. It's compounded semiannually, so $n=2$ . Since it's a one-year CD, $t=1$ . Plug the values into the formula for Bank A: $A=P(1+(0.074/2))^{(2*1)}$ . Calculate the expression inside the parentheses for Bank A: $1+(0.074/2) = 1+0.037 = 1.037$ . Now raise this to the power of $2$ for Bank A: $(1.037)^2 = 1.0757$ approximately. Since $P$ is the same for both banks and we're looking for the rate, we can ignore $P$ for now. The APY for Bank A is approximately $0.074$ $0$ or $0.074$ $1$ .
Compare APYs for better deal: Bank A's interest rate is $7.4\%$ or $0.074$ as a decimal. It's compounded semiannually, so $n=2$ . Since it's a one-year CD, $t=1$ . Plug the values into the formula for Bank A: $A=P(1+(0.074/2))^{(2*1)}$ . Calculate the expression inside the parentheses for Bank A: $1+(0.074/2) = 1+0.037 = 1.037$ . Now raise this to the power of $2$ for Bank A: $(1.037)^2 = 1.0757$ approximately. Since $P$ is the same for both banks and we're looking for the rate, we can ignore $P$ for now. The APY for Bank A is approximately $0.074$ $0$ or $0.074$ $1$ . Now let's calculate for Bank B. Bank B's interest rate is $0.074$ $2$ or $0.074$ $3$ as a decimal. It's compounded daily, so $0.074$ $4$ . Since it's a one-year CD, $t=1$ .
Compare APYs for better deal: Bank A's interest rate is $7.4\%$ or $0.074$ as a decimal. It's compounded semiannually, so $n=2$ . Since it's a one-year CD, $t=1$ . Plug the values into the formula for Bank A: $A=P(1+(0.074/2))^{(2*1)}$ . Calculate the expression inside the parentheses for Bank A: $1+(0.074/2) = 1+0.037 = 1.037$ . Now raise this to the power of $2$ for Bank A: $(1.037)^2 = 1.0757$ approximately. Since $P$ is the same for both banks and we're looking for the rate, we can ignore $P$ for now. The APY for Bank A is approximately $0.074$ $0$ or $0.074$ $1$ . Now let's calculate for Bank B. Bank B's interest rate is $0.074$ $2$ or $0.074$ $3$ as a decimal. It's compounded daily, so $0.074$ $4$ . Since it's a one-year CD, $t=1$ . Plug the values into the formula for Bank B: $0.074$ $6$ .
Compare APYs for better deal: Bank A's interest rate is $7.4\%$ or $0.074$ as a decimal. It's compounded semiannually, so $n=2$ . Since it's a one-year CD, $t=1$ . Plug the values into the formula for Bank A: $A=P(1+(0.074/2))^{(2*1)}$ . Calculate the expression inside the parentheses for Bank A: $1+(0.074/2) = 1+0.037 = 1.037$ . Now raise this to the power of $2$ for Bank A: $(1.037)^2 = 1.0757$ approximately. Since $P$ is the same for both banks and we're looking for the rate, we can ignore $P$ for now. The APY for Bank A is approximately $0.074$ $0$ or $0.074$ $1$ . Now let's calculate for Bank B. Bank B's interest rate is $0.074$ $2$ or $0.074$ $3$ as a decimal. It's compounded daily, so $0.074$ $4$ . Since it's a one-year CD, $t=1$ . Plug the values into the formula for Bank B: $0.074$ $6$ . Calculate the expression inside the parentheses for Bank B: $0.074$ $7$ approximately.
Compare APYs for better deal: Bank A's interest rate is $7.4\%$ or $0.074$ as a decimal. It's compounded semiannually, so $n=2$ . Since it's a one-year CD, $t=1$ . Plug the values into the formula for Bank A: $A=P(1+(0.074/2))^{(2*1)}$ . Calculate the expression inside the parentheses for Bank A: $1+(0.074/2) = 1+0.037 = 1.037$ . Now raise this to the power of $2$ for Bank A: $(1.037)^2 = 1.0757$ approximately. Since $P$ is the same for both banks and we're looking for the rate, we can ignore $P$ for now. The APY for Bank A is approximately $0.074$ $0$ or $0.074$ $1$ . Now let's calculate for Bank B. Bank B's interest rate is $0.074$ $2$ or $0.074$ $3$ as a decimal. It's compounded daily, so $0.074$ $4$ . Since it's a one-year CD, $t=1$ . Plug the values into the formula for Bank B: $0.074$ $6$ . Calculate the expression inside the parentheses for Bank B: $0.074$ $7$ approximately. Now raise this to the power of $0.074$ $8$ for Bank B: $0.074$ $9$ .
Compare APYs for better deal: Bank A's interest rate is $7.4\%$ or $0.074$ as a decimal. It's compounded semiannually, so $n=2$ . Since it's a one-year CD, $t=1$ . Plug the values into the formula for Bank A: $A=P(1+(0.074/2))^{(2*1)}$ . Calculate the expression inside the parentheses for Bank A: $1+(0.074/2) = 1+0.037 = 1.037$ . Now raise this to the power of $2$ for Bank A: $(1.037)^2 = 1.0757$ approximately. Since $P$ is the same for both banks and we're looking for the rate, we can ignore $P$ for now. The APY for Bank A is approximately $0.074$ $0$ or $0.074$ $1$ . Now let's calculate for Bank B. Bank B's interest rate is $0.074$ $2$ or $0.074$ $3$ as a decimal. It's compounded daily, so $0.074$ $4$ . Since it's a one-year CD, $t=1$ . Plug the values into the formula for Bank B: $0.074$ $6$ . Calculate the expression inside the parentheses for Bank B: $0.074$ $7$ approximately. Now raise this to the power of $0.074$ $8$ for Bank B: $0.074$ $9$ . The calculation for Bank B is a bit more complex, so we might use a calculator. $n=2$ $0$ .
Compare APYs for better deal: Bank A's interest rate is $7.4\%$ or $0.074$ as a decimal. It's compounded semiannually, so $n=2$ . Since it's a one-year CD, $t=1$ . Plug the values into the formula for Bank A: $A=P(1+(0.074/2))^{(2*1)}$ . Calculate the expression inside the parentheses for Bank A: $1+(0.074/2) = 1+0.037 = 1.037$ . Now raise this to the power of $2$ for Bank A: $(1.037)^2 = 1.0757$ approximately. Since $P$ is the same for both banks and we're looking for the rate, we can ignore $P$ for now. The APY for Bank A is approximately $0.074$ $0$ or $0.074$ $1$ . Now let's calculate for Bank B. Bank B's interest rate is $0.074$ $2$ or $0.074$ $3$ as a decimal. It's compounded daily, so $0.074$ $4$ . Since it's a one-year CD, $t=1$ . Plug the values into the formula for Bank B: $0.074$ $6$ . Calculate the expression inside the parentheses for Bank B: $0.074$ $7$ approximately. Now raise this to the power of $0.074$ $8$ for Bank B: $0.074$ $9$ . The calculation for Bank B is a bit more complex, so we might use a calculator. $n=2$ $0$ . The APY for Bank B is approximately $n=2$ $1$ or $n=2$ $2$ .
Compare APYs for better deal: Bank A's interest rate is $7.4\%$ or $0.074$ as a decimal. It's compounded semiannually, so $n=2$ . Since it's a one-year CD, $t=1$ . Plug the values into the formula for Bank A: $A=P(1+(0.074/2))^{(2*1)}$ . Calculate the expression inside the parentheses for Bank A: $1+(0.074/2) = 1+0.037 = 1.037$ . Now raise this to the power of $2$ for Bank A: $(1.037)^2 = 1.0757$ approximately. Since $P$ is the same for both banks and we're looking for the rate, we can ignore $P$ for now. The APY for Bank A is approximately $0.074$ $0$ or $0.074$ $1$ . Now let's calculate for Bank B. Bank B's interest rate is $0.074$ $2$ or $0.074$ $3$ as a decimal. It's compounded daily, so $0.074$ $4$ . Since it's a one-year CD, $t=1$ . Plug the values into the formula for Bank B: $0.074$ $6$ . Calculate the expression inside the parentheses for Bank B: $0.074$ $7$ approximately. Now raise this to the power of $0.074$ $8$ for Bank B: $0.074$ $9$ . The calculation for Bank B is a bit more complex, so we might use a calculator. $n=2$ $0$ . The APY for Bank B is approximately $n=2$ $1$ or $n=2$ $2$ . Comparing the APYs, Bank A's $0.074$ $1$ is slightly higher than Bank B's $n=2$ $2$ . So, Bank A offers the better deal.