Question

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, how much more money would lily have in her account than arianna, to the nearest dollar?

Answer 1

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.