Respuesta :
The sum of the balances of these accounts at the end of 5 years is given by: Option B: $53,901.59 (approx)
How to calculate compound interest's amount?
If the initial amount (also called as principal amount) is P, and the interest rate is R% per unit time, and it is left for T unit of time for that compound interest, then the interest amount earned is given by:
[tex]CI = P(1 +\dfrac{R}{100})^T - P[/tex]
The final amount becomes:
[tex]A = CI + P\\A = P(1 +\dfrac{R}{100})^T[/tex]
How to calculate simple interest amount?
If the initial amount (also called as principal amount) is P, and the interest rate is R% annually, and it is left for T years for that simple interest, then the interest amount earned is given by:
[tex]I = \dfrac{P \times R \times T}{100}[/tex]
For the considered case, we're given that:
- Initial amount in both accounts deposited = $24,000 = P
- Type of interest: Compound interest in first account and simple interest in second account
- Unit of time: Annually
- Rate of interest = 2.4% annually = R
- Total unit of time for which amount is to be calculated: 5 years = T
In first account, the final amount at the end of 5 years is evaluated as:
[tex]A = 24000(1 + \dfrac{2.4}{100})^4 = 24000(1.024)^4 \approx 27021.59\: \rm (in \: dollars)[/tex]
In second account, the final amount at the end of 5 years is evaluated as:
[tex]A = 24000 + \dfrac{24000 \times 2.4 \times 5}{100} = 24000 + 2880 = 26880 \text{\: (in dollars)}[/tex]
Total amount after 5 years in these accounts = [tex]27021.59 + 26880 = 53901.59[/tex] (in dollars)
Thus, the sum of the balances of these accounts at the end of 5 years is given by: Option B: $53,901.59 (approx)
Learn more about compound interest here:
https://brainly.com/question/11897800
