The sum of the balances of these accounts at the end of 5 years is given by: Option B: $53,901.59 (approx)
<h3>How to calculate compound interest's amount?</h3>
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:
![CI = P(1 +\dfrac{R}{100})^T - P](https://tex.z-dn.net/?f=CI%20%3D%20P%281%20%2B%5Cdfrac%7BR%7D%7B100%7D%29%5ET%20-%20P)
The final amount becomes:
![A = CI + P\\A = P(1 +\dfrac{R}{100})^T](https://tex.z-dn.net/?f=A%20%3D%20CI%20%2B%20P%5C%5CA%20%3D%20P%281%20%2B%5Cdfrac%7BR%7D%7B100%7D%29%5ET)
<h3>How to calculate simple interest amount?</h3>
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:
![I = \dfrac{P \times R \times T}{100}](https://tex.z-dn.net/?f=I%20%3D%20%5Cdfrac%7BP%20%5Ctimes%20R%20%5Ctimes%20T%7D%7B100%7D)
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:
![A = 24000(1 + \dfrac{2.4}{100})^4 = 24000(1.024)^4 \approx 27021.59\: \rm (in \: dollars)](https://tex.z-dn.net/?f=A%20%3D%2024000%281%20%2B%20%5Cdfrac%7B2.4%7D%7B100%7D%29%5E4%20%3D%2024000%281.024%29%5E4%20%20%5Capprox%2027021.59%5C%3A%20%5Crm%20%28in%20%5C%3A%20%20dollars%29)
In second account, the final amount at the end of 5 years is evaluated as:
![A = 24000 + \dfrac{24000 \times 2.4 \times 5}{100} = 24000 + 2880 = 26880 \text{\: (in dollars)}](https://tex.z-dn.net/?f=A%20%3D%2024000%20%2B%20%20%5Cdfrac%7B24000%20%5Ctimes%202.4%20%5Ctimes%205%7D%7B100%7D%20%3D%2024000%20%2B%202880%20%3D%2026880%20%5Ctext%7B%5C%3A%20%28in%20dollars%29%7D)
Total amount after 5 years in these accounts =
(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:
brainly.com/question/11897800