Find the ending balance in an account that opens with $9,000, earns 4.5% interest compounded quarterly, and is held for 5 years. (Round your answer to the nearest cent.)
To find the ending balance in the account, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A = the ending balance
P = the principal amount (initial deposit)
r = the annual interest rate (in decimal form)
n = the number of times interest is compounded per year
t = the number of years
In this case, the initial deposit (principal amount) is $9,000, the annual interest rate is 4.5% (or 0.045 in decimal form), the interest is compounded quarterly (n = 4), and the investment is held for 5 years.
Applying these values to the formula, we have:
A = 9000(1 + 0.045/4)^(4*5)
Now, let's calculate step by step:
Step 1: Divide the annual interest rate by the number of times interest is compounded per year:
0.045/4 = 0.01125
Step 2: Add 1 to the result:
1 + 0.01125 = 1.01125
Step 3: Multiply the result by the number of times interest is compounded per year (4):
1.01125^4 = 1.0464491
Step 4: Multiply the result by the number of years (5):
1.0464491^5 = 1.23037805
Step 5: Multiply the result by the principal amount:
1.23037805 * 9000 = 11073.41
Therefore, the ending balance in the account, rounded to the nearest cent, is $11,073.41.