Respuesta :
Answer: $13,114
Step-by-step explanation:
We would apply the formula for determining compound interest which is expressed as
A = P(1+r/n)^nt
Where
A = total amount in the account at the end of t years
r represents the interest rate.
n represents the periodic interval at which it was compounded.
P represents the principal or initial amount deposited
From the information given,
P = 9000
r = 3.8% = 3.8/100 = 0.038
n = 2 because it was compounded 2 times in a year.
t = 10 years
Therefore,.
A = 9000(1+0.038/2)^2 × 10
A = 9000(1+0.019)^20
A = 9000(1.019)^20
A = $13114
The final amount that Jenny's investment would be worth of at the end of 10 years is given by: Option B: $13114 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]
For this case, we are given that:
- Initial amount Jenny invested = $9,000 = P
- The rate of interest = 3.8% semi annually (0.5 years) = 3.8/2 = 1.9% per 0.5 years = R
- Thus, unit of time = half year
- Time for which investment was made= 10 years = 20 half years =T
Thus, the final amount at the end of 10 years is given by:
[tex]A = P(1 +\dfrac{1.9}{100})^T\\\\A = 9000(1 + \dfrac{1.9}{100})^{20} = 9000(1.019)^{20} \approx 13114 \text{\: \: (in dollars)}[/tex]
Thus, the final amount that Jenny's investment would be worth of at the end of 10 years is given by: Option B: $13114 approx.
Learn more about compound interest here:
https://brainly.com/question/11897800
