Using the compound interest formula
A = P (1+ ((r)/ (n)) ^nt
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.)
$18,000 is invested in an account paying 3% interest compounded quarterly.
A = 18,000*(1.0075)^40
If you don't have a calculator to do that, you can use Google:
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To find the amount of money in the account at the end of 10 years, we need to use the compound interest formula:
A = P(1 + (r/n))^(nt)
where:
A = Amount of money in the account at the end of the time period
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, we are given:
P = $18,000 (the initial investment)
r = 3% (annual interest rate, expressed as a decimal, so 3% = 0.03)
n = 4 (since interest is compounded quarterly, there are 4 quarters in a year)
t = 10 (number of years)
Let's substitute these values into the formula:
A = $18,000(1 + (0.03/4))^(4*10)
Now, let's simplify the equation inside the parentheses:
A = $18,000(1 + (0.0075))^(40)
A = $18,000(1.0075)^(40)
Next, let's calculate 1.0075 raised to the power of 40:
A = $18,000(1.3563)
Finally, let's calculate the numerical amount:
A = $18,000 * 1.3563
A ≈ $24,413.40
Therefore, the amount of money in the account at the end of 10 years will be approximately $24,413.40.