Use the compound interest formula to solve:
$18,000 is invested in an account paying 3% interest compounded quarterly.
Find the amount of money in the account at the end of 10 years. (Show values substituted in the formula, and calculate the numerical amount.)
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To solve this problem using the compound interest formula, we will use the following formula:
A = P(1 + r/n)^(nt)
Where:
A = final amount
P = principal amount (initial investment)
r = annual interest rate (as a decimal)
n = number of times the interest is compounded per year
t = number of years
In this case:
P = $18,000
r = 3% = 0.03 (converted to decimal)
n = 4 (compounded quarterly)
t = 10 years
Substituting the values into the formula, we get:
A = $18,000(1 + 0.03/4)^(4*10)
Now let's calculate this expression step by step:
A = $18,000(1 + 0.0075)^(40)
A = $18,000(1.0075)^(40)
Now we can calculate the amount using a calculator or a spreadsheet. Raising a number to the power of 40 might be a bit tedious, but most calculators and spreadsheets have a built-in function for this.
Using a calculator, we find:
A ≈ $24,754.61
Therefore, the amount of money in the account at the end of 10 years will be approximately $24,754.61.