Final answer:
The final amount in the account after 9 years will be $10,455.36.
Step-by-step explanation:
To find the final amount of money in an account with an initial deposit of $8,300 at an interest rate of 2.5% compounded quarterly over 9 years, we use the formula for compound interest:
A = P(1 + \frac{r}{n})^{nt}
Where:
- A is the amount of money accumulated after n years, including interest.
- P is the principal amount (the initial amount of money).
- r is the annual interest rate (decimal).
- n is the number of times that interest is compounded per year.
- t is the time the money is invested for, in years.
For this question:
- P = $8,300
- r = 2.5% or 0.025 (as a decimal)
- n = 4 (because interest is compounded quarterly)
- t = 9 years
Plugging these values into the formula gives us:
A = 8300(1 + \frac{0.025}{4})^(4\times9)
Calculating the compounded amount:
A = 8300(1 + 0.00625)^(36)
A = 8300(1.00625)^36
A = 8300 \times 1.259707
A = $10,455.36 (rounded to two decimal places)
Therefore, the final amount in the account after 9 years will be $10,455.36.