Final answer:
Arianna invested $250 in an account paying an interest rate of 8(¼)% compounded continuously. Lily invested $250 in an account paying an interest rate of 8(¾)% compounded quarterly. After 18 years, Lily would have approximately $96 more in her account than Arianna.
Step-by-step explanation:
Arianna invested $250 in an account paying an interest rate of 8(¼)% compounded continuously. Lily invested $250 in an account paying an interest rate of 8(¾)% compounded quarterly. To find out how much more money Lily would have in her account than Arianna after 18 years, we can use the compound interest formula:
A = P * e^(rt)
Where:
A = Final amount
P = Principal amount (initial investment)
e = Euler's number (approximately 2.71828)
r = Annual interest rate (as a decimal)
t = Time period in years
For Arianna:
A = 250 * e^(0.0825*18)
For Lily:
A = 250 * (1 + 0.0875/4)^(4*18)
Calculating these values, we find that after 18 years, Arianna would have approximately $1419 and Lily would have approximately $1515. Therefore, Lily would have approximately $96 more in her account than Arianna.