Final answer:
To find the total amount in the savings account after 6 years with a principal of $9,000 and a 3% interest rate compounded quarterly, one can use the compound interest formula. After calculating, the final amount is approximately $10,774.95.
Step-by-step explanation:
The question asks to find the total amount in a savings account after $9,000 is invested at a 3% interest rate compounded quarterly over 6 years. To solve this, the formula for compound interest is used:
A = P(1 + 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 number of years the money is invested for.
Plugging in the values:
A = $9,000(1 + 0.03/4)(4*6)
A = $9,000(1 + 0.0075)24
A = $9,000(1.0075)24
Calculating the value using a calculator gives us:
A ≈ $9,000 * 1.197217
A ≈ $10,774.95
Therefore, the total amount in the savings account after 6 years would be approximately $10,774.95.