Find the accumulated amount A, if the principal P is invested at an interest rate of r per year for t years.
P = $2500, r = 3%, t = 3, compounded quarterly
$ ?
A = P(1+r/n)^(n*t)
= 2500(1+.03/4)^(4*3)
= 2734.52
To find the accumulated amount A, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
where:
A = accumulated amount
P = principal
r = interest rate per year (as a decimal)
t = number of years
n = number of times interest is compounded per year
In this case:
P = $2500
r = 3% = 0.03 (as a decimal)
t = 3 years
n = 4 (compounded quarterly)
Substituting these values into the formula:
A = 2500(1 + 0.03/4)^(4 * 3)
Simplifying inside the parentheses first:
A = 2500(1 + 0.0075)^(12)
Calculating the value inside the parentheses:
A = 2500(1.0075)^(12)
Using a calculator, we find:
A ≈ $2,626.80
So, the accumulated amount A is approximately $2,626.80.
To find the accumulated amount A, we can use the formula for compound interest:
A = P * (1 + r/n)^(n*t)
Where:
A = Accumulated amount (the amount you want to find)
P = Principal amount (initial investment)
r = Interest rate (expressed as a decimal)
n = Number of times interest is compounded per year
t = Number of years
In your case, P = $2500, r = 3% (or 0.03 as a decimal), t = 3, and the interest is compounded quarterly. This means n = 4 because there are 4 quarters in a year.
Now let's plug in these values in the formula to find A:
A = 2500 * (1 + 0.03/4)^(4*3)
First, let's simplify the expression inside the parentheses:
1 + 0.03/4 = 1 + 0.0075 = 1.0075
Now, let's simplify the exponent part:
4 * 3 = 12
So the formula becomes:
A = 2500 * (1.0075)^12
Evaluating this expression, we find:
A ≈ $2797.8694
Therefore, the accumulated amount A after 3 years, with an initial investment of $2500 at an interest rate of 3% compounded quarterly, is approximately $2797.87.