Final answer:
To calculate the accumulated amount for a principal of $290,000 at an annual interest rate of 3.5% for 3 years, compounded daily, use the formula A = P(1 + r/n)^(nt) with n=365. Convert the interest rate to decimal and substitute the values to find A.
Step-by-step explanation:
To find the accumulated amount A when the principal P is invested at an interest rate r per year for t years, compounded daily, we use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
P is the principal amount ($290,000)
r is the annual interest rate (3.5% or 0.035 in decimal form)
n is the number of times interest is compounded per year (365, since it's daily)
t is the number of years the money is invested (3 years)
First, we'll convert the interest rate to a decimal and divide by 365:
r/n = 0.035/365
Next, apply the values to the formula:
A = 290,000(1 + 0.035/365)^(365*3)
Calculate the accumulated amount A, and round to the nearest cent:
A ≈ $290,000(1 + 0.0000958904)^(1095)
A ≈ $290,000(1.0000958904)^1095
A ≈ $290,000 * (1.109667)
A ≈ $321,803.43
Thus, the accumulated amount after 3 years is $321,803.43.