Find the accumulated amount A if the principal P = $3,000 is invested at the interest rate of r = 9% per year for t = 5 years, compounded annually. Please round your answer to the nearest cent.
A = Po(1+r)^n.
Po = $3,000. = Initial investment.
r = 9% / 100% = 0.09 = APR expressed as a decimal.
n = 1Comp./yr * 5yrs = 5 Compounding
periods.
To find the accumulated amount A when the principal P is invested at an interest rate of r compounded annually for t years, you can use the formula for compound interest:
A = P * (1 + r)^t
Given that P = $3,000, r = 9% (or 0.09 as a decimal), and t = 5, we can substitute these values into the formula:
A = $3,000 * (1 + 0.09)^5
To simplify this calculation, we first need to evaluate the expression inside the parentheses:
(1 + 0.09) = 1.09
Now we can substitute this value back into the formula:
A = $3,000 * 1.09^5
Using a calculator:
A = $3,000 * 1.62889
A ≈ $4,886.67
Therefore, the accumulated amount, rounded to the nearest cent, is approximately $4,886.67.