Use the compound interest formula
$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.)
The formula for the value after ten years is 18,000*(1.0075)^40, because there are 40 interest-paying events and each time the principal increases by a factor 1.0075, as 1/4 of 3% is added.
Now do the calculation
Would it be $24,270.28 ?
Yes, that's what I get, too
To find the amount of money in the account at the end of 10 years using the compound interest formula, we can use the formula:
A = P(1 + r/n)^(nt)
Where:
A = amount of money accumulated at the end of the investment 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 the money is invested for
Given:
P = $18,000
r = 3% = 0.03 (converted to decimal)
n = 4 (compounded quarterly)
t = 10 years
Substituting these values into the formula, we have:
A = $18,000(1 + 0.03/4)^(4*10)
Simplifying the formula further:
A = $18,000(1.0075)^40
Calculating the numerical amount:
A ≈ $18,000(1.36837)
A ≈ $24,629.66
Therefore, the amount of money in the account at the end of 10 years is approximately $24,629.66, rounded to two decimal places.