Annabelle invested $37,000 in an account paying an interest rate of 8$\frac{3}{8}$% compounded continuously. Nevaeh invested $37,000 in an account paying an interest rate of 8$\frac{1}{4}$% compounded annually.

After 17 years, how much more money would Annabelle have in her account than Nevaeh, to the nearest dollar?

A. $15,218
B. $14,218
C. $16,218
D. $13,218

Annabelle's investment is compounded continuously, while Nevaeh's is compounded annually. Continuous compounding typically yields slightly more interest over time due to the compounding effect being more frequent.

To calculate Annabelle's future value, we use the continuous compounding formula: A = P * e^(rt), where A is the amount of money accumulated after n years, P is the principal amount, r is the annual interest rate (in decimal), t is the time in years, and e is the base of the natural logarithm. For Nevaeh, we use the standard compound interest formula: A = P * (1 + r/n)^(nt), where n is the number of times interest is compounded per time period.

For Annabelle: A = $37,000 * e^(0.08375 * 17) ≈ $114,218.08

For Nevaeh: A = $37,000 * (1 + 0.0825/100)^(1*17) ≈ $99,000.49

The difference between Annabelle's and Nevaeh's amounts after 17 years is approximately $114,218.08 - $99,000.49 ≈ $15,217.59. Rounded to the nearest dollar,

Annabelle would have approximately $15,218 more in her account than Nevaeh. Therefore, the correct answer is option a. $15,218