Respuesta :
The amount, to the nearest hundred dollars, that would be in the account of Serenity after 9 years for the considered situation is $20,836.162
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]
For this case, we're specified that:
- Initial amount that was deposited = P = $16,000
- Rate of interest = R = 4.5 (in percent) annually (compount interest)
- So, unit of time = 1 year.
- Number of units of time for which money was invested = 9 (years).
Thus, we get the final amount in the account of Serenity after 9 years as evaluated by:
[tex]A = P(1 +\dfrac{R}{100})^T\\\\A = 16000 \times\left(1+\dfrac{4.5}{100}\right)^6 = 16000 \times (1.045)^6\\\\A = 20836.162 \: \rm dollars[/tex]
Thus, the amount, to the nearest hundred dollars, that would be in the account of Serenity after 9 years for the considered situation is $20,836.162
Learn more about compound interest here:
https://brainly.com/question/11897800
