Magan invested \( \$ 210 \) in an account paying an interest rate of \( 9 \frac{5}{8} \% \) compounded quarterly. Myesha invested \( \$ 210 \) in an account paying an interest rate of \( 9 \frac{7}{8} \% \) compounded continuously After 9 years, how much more money would Myesha have in her account than Magan, to the nearest dollar?

To solve this problem, we first need to calculate the future value of both investments after 9 years. **Magan's Investment:** For Magan, who has an interest rate of \( 9 \frac{5}{8} \% = 9.625\% = 0.09625 \) compounded quarterly, we can use the formula for compound interest: \[ A = P \left(1 + \frac{r}{n}\right)^{nt} \] Where: - \( A \) is the amount of money accumulated after n years, including interest. - \( P \) is the principal amount (the initial amount). - \( r \) is the annual interest rate (decimal). - \( n \) is the number of times that interest is compounded per year. - \( t \) is the time the money is invested for in years. In this case: - \( P = 210 \) - \( r = 0.09625 \) - \( n = 4 \) (quarterly) - \( t = 9 \) Calculating Magan’s amount: \[ A_M = 210 \left(1 + \frac{0.09625}{4}\right)^{4 \times 9} \] \[ = 210 \left(1 + 0.0240625\right)^{36} \] \[ = 210 \left(1.0240625\right)^{36} \] \[ = 210 \times 2.4363 \approx 511.62 \] **Myesha's Investment:** Myesha's investment uses the formula for continuously compounded interest: \[ A = Pe^{rt} \] Where: - \( e \) is Euler's number (approximately equal to \( 2.71828 \)). - \( P \) is the principal amount. - \( r \) is the annual interest rate (decimal). - \( t \) is the time the money is invested for in years. For Myesha: - \( P = 210 \) - \( r = 9.875\% = 0.09875 \) - \( t = 9 \) Calculating Myesha’s amount: \[ A_Y = 210e^{0.09875 \times 9} \] \[ = 210e^{0.88875} \] \[ \approx 210 \times 2.4265 \approx 509.57 \] **Calculating the Difference:** Now, we can find the difference between Myesha's and Magan's totals: \[ \text{Difference} = A_Y - A_M = 511.62 - 509.57 \approx 2.05 \] After rounding to the nearest dollar, Myesha would have approximately **$2 more** than Magan.