Questions: Person A deposits 2800 in an account that pays 6% interest compounded once a year. Person B deposits 2550 in an account that pays 7% interest compounded monthly. Complete parts (a) through (c) below. a. Who will have more money in their account after one year? How much more? Select the correct choice below and fill in the answer box within your choice. (Round to the nearest dollar as needed.) A. Person A will have 234 more than Person B. B. Person B will have more than Person A b. Who will have more money in their account after five years? How much more? Select the correct choice below and fill in the answer box within your choice. (Round to the nearest dollar as needed.) A. Person B will have more than Person A. B. Person A will have more than Person B.

Person A deposits 2800 in an account that pays 6% interest compounded once a year. Person B deposits 2550 in an account that pays 7% interest compounded monthly. Complete parts (a) through (c) below. a. Who will have more money in their account after one year? How much more? Select the correct choice below and fill in the answer box within your choice. (Round to the nearest dollar as needed.) A. Person A will have 234 more than Person B. B. Person B will have more than Person A b. Who will have more money in their account after five years? How much more? Select the correct choice below and fill in the answer box within your choice. (Round to the nearest dollar as needed.) A. Person B will have more than Person A. B. Person A will have more than Person B.
Transcript text: Person A deposits $\$ 2800$ in an account that pays $6 \%$ interest compounded once a year. Person B deposits $\$ 2550$ in an account that pays $7 \%$ interest compounded monthly. Complete parts (a) through (c) below. a. Who will have more money in their account after one year? How much more? Select the correct choice below and fill in the answer box within your choice. (Round to the nearest dollar as needed.) A. Person A will have $\$ 234$ more than Person B. B. Person B will have \$ more than Person A b. Who will have more money in their account after five years? How much more? Select the correct choice below and fill in the answer box within your choice. (Round to the nearest dollar as needed.) A. Person B will have $\$$ $\square$ more than Person A . B. Person A will have $\$$ $\square$ more than Person B.
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Solution

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Solution Steps

Step 1: Calculate the Future Value for Each Person

Using the formula for compound interest, $FV = P(1 + \frac{r}{n})^{nt}$, we calculate the future values. For Person A: $FV_A = 2800(1 + \frac{0.06}{1})^{1_1} = 2968$ For Person B: $FV_B = 2550(1 + \frac{0.07}{12})^{12_1} = 2734$

Step 2: Compare the Future Values

After comparing the future values, Person A will have more money in their account by $234 after 1 years.

Final Answer:

Person A will have more money by $234, with their future value being $2968 compared to $2734.

Step 1: Calculate the Future Value for Each Person

Using the formula for compound interest, $FV = P(1 + \frac{r}{n})^{nt}$, we calculate the future values. For Person A: $FV_A = 2800(1 + \frac{0.06}{1})^{1_5} = 3747$ For Person B: $FV_B = 2550(1 + \frac{0.07}{12})^{12_5} = 3615$

Step 2: Compare the Future Values

After comparing the future values, Person A will have more money in their account by $132 after 5 years.

Final Answer:

Person A will have more money by $132, with their future value being $3747 compared to $3615.

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