222k views
2 votes
Charlotte invested $730 in an account paying an interest rate of 3, one half3 2 1 ​ % compounded continuously. khalil invested $730 in an account paying an interest rate of 3, start fraction, 7, divided by, 8, end fraction3 8 7 ​ % compounded daily. after 8 years, how much more money would khalil have in his account than charlotte, to the nearest dollar?

User Yuwen Yan
by
7.7k points

1 Answer

2 votes

Final answer:

To determine how much more money Khalil will have in his account compared to Charlotte after 8 years, we need to apply the formulas for continuous and daily compounding interest to their respective investments and find the difference.

Step-by-step explanation:

We need to calculate the future value of investments for Charlotte and Khalil using their respective interest rates and methods of compounding. To do so, we'll use the formulas for continuous compounding and daily compounding and compare the results after 8 years.

Charlotte's investment grows at a continuous rate, given by the formula A = Pert, where P is the principal amount, e is the base of the natural logarithm, r is the interest rate, and t is the time in years. Khalil's investment grows with daily compounding, and the formula for this method is A = P(1 + r/n)nt, where n is the number of times the interest is compounded per year.

For Charlotte:
A = 730e(0.0325)(8)

For Khalil, assuming there are 365 days in a year:
A = 730(1 + 0.0375/365)(365)(8)

We then calculate the amount in each account after 8 years, and the difference will give us how much more money Khalil will have in his account compared to Charlotte. Our final step is to round the result to the nearest dollar.

User Thales
by
7.8k points