Aubrey invested \( \$ 150 \) in an account paying an interest rate of \( 6 \frac{5}{8} \% \) compounded monthly. Miguel invested \( \$ 150 \) in an account paying an interest rate of \( 6 \frac{1}{4} \% \) compounded daily. After 7 years, how much more money would Aubrey have in her account than Miguel, to the nearest dollar?

To determine how much more money Aubrey would have in her account compared to Miguel after 7 years, we'll calculate the future value of both investments using the compound interest formula: \[ A = P \left(1 + \frac{r}{n}\right)^{nt} \] Where: - \( A \) = the amount of money accumulated after \( t \) years, including interest. - \( P \) = the principal amount (\$150 for both investors). - \( r \) = annual interest rate (in decimal). - \( n \) = number of times that interest is compounded per year. - \( t \) = time the money is invested for in years. ### Aubrey's Investment - **Principal (\( P \))**: \$150 - **Annual Interest Rate (\( r \))**: \( 6 \frac{5}{8}\% = 6.625\% = 0.06625 \) - **Compounded Monthly (\( n \))**: 12 times a year - **Time (\( t \))**: 7 years Plugging these values into the formula: \[ A_{\text{Aubrey}} = 150 \left(1 + \frac{0.06625}{12}\right)^{12 \times 7} \] \[ A_{\text{Aubrey}} \approx 150 \times (1.0055208333)^{84} \] \[ A_{\text{Aubrey}} \approx 150 \times 1.588 \] \[ A_{\text{Aubrey}} \approx \$238.20 \] ### Miguel's Investment - **Principal (\( P \))**: \$150 - **Annual Interest Rate (\( r \))**: \( 6 \frac{1}{4}\% = 6.25\% = 0.0625 \) - **Compounded Daily (\( n \))**: 365 times a year - **Time (\( t \))**: 7 years Plugging these values into the formula: \[ A_{\text{Miguel}} = 150 \left(1 + \frac{0.0625}{365}\right)^{365 \times 7} \] \[ A_{\text{Miguel}} \approx 150 \times (1.0001712329)^{2555} \] \[ A_{\text{Miguel}} \approx 150 \times 1.548 \] \[ A_{\text{Miguel}} \approx \$232.26 \] ### Difference in Amounts \[ \text{Difference} = A_{\text{Aubrey}} - A_{\text{Miguel}} \] \[ \text{Difference} \approx 238.20 - 232.26 \] \[ \text{Difference} \approx \$5.94 \] Rounding to the nearest dollar: **Aubrey would have approximately \$6 more than Miguel after 7 years.** **Answer:** $6