Question

Kevin invested $860 in an account paying an interest rate of 4, start fraction, 5, divided by, 8, end fraction4 8 5 ​ % compounded continuously. deondra invested $860 in an account paying an interest rate of 4, start fraction, 7, divided by, 8, end fraction4 8 7 ​ % compounded monthly. after 17 years, how much more money would deondra have in her account than kevin, to the nearest dollar?

Answer 1

Kevin would have approximately $2088.06 and Deondra would have approximately $2146.35 after 17 years. So, Deondra would have around $58.29 more money in her account than Kevin.

Step-by-step explanation:

To calculate the future value of an amount compounded continuously, we use the formula P * e^(rt), where P is the principal amount, e is Euler's constant ≈ 2.71828, r is the interest rate as a decimal, and t is the time in years. For Kevin's investment, we have P = $860, r = 4.625%, and t = 17 years. Plugging these values into the formula, we get FV = 860 * e^(0.04625 * 17) ≈ $2088.06. For Deondra's investment, we have r = 4.875% compounded monthly. Using the formula FV = P * (1 + r/n)^(nt), where n is the number of compounding periods per year, we find FV = 860 * (1 + 0.04875/12)^(12 * 17) ≈ $2146.35.

Therefore, Deondra would have approximately $2146.35 - $2088.06 = $58.29 more money in her account than Kevin after 17 years.

Answer 2

Deondra would have approximately $36,236 more in her account than Kevin after 17 years.

How to solve

To determine the difference in the future value of Kevin's and Deondra's accounts after 17 years, follow these steps:

1. Calculate the annual interest rates:

Kevin's annual interest rate = 4.5% / 100 = 0.045

Deondra's annual interest rate = 4.7% / 100 = 0.047

2. Calculate the monthly interest rates:

Kevin's monthly interest rate = 0.045 / 12 = 0.00375

Deondra's monthly interest rate = 0.047 / 12 = 0.00391667

3. Calculate the number of compounding periods for each account:

Kevin's compounding periods = 17 years * 12 months/year = 204 months

Deondra's compounding periods = 17 years * 12 months/year = 204 months

4. Calculate the future value of each account:

Kevin's future value = Principal * (1 + Monthly interest rate)^(Number of compounding periods)

Kevin's future value = $860 * (1 + 0.00375)^204 ≈ $2,420,870.31

Deondra's future value = Principal * (1 + Monthly interest rate)^(Number of compounding periods)

Deondra's future value = $860 * (1 + 0.00391667)^204 ≈ $2,457,105.84

5. Calculate the difference in future values:

Difference = Deondra's future value - Kevin's future value

Difference = $2,457,105.84 - $2,420,870.31 ≈ $36,235.53

6. Round the difference to the nearest dollar:

Difference rounded = $36,235.53 ≈ $36,236

Therefore, Deondra would have approximately $36,236 more in her account than Kevin after 17 years.