Find the value after 5 years of a $3000. Savings account that pays three percent interest compounded yearly round the answer to two decimal places.
To calculate the value after 5 years, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A = the final amount
P = the principal amount (initial deposit)
r = annual interest rate (as a decimal)
n = number of times that interest is compounded per year
t = number of years
In this case, P = $3000, r = 0.03 (3% expressed as a decimal), n = 1 (compounded yearly), and t = 5. Plugging these values into the formula:
A = 3000(1 + 0.03/1)^(1*5)
A = 3000(1 + 0.03)^5
A = 3000(1.03)^5
A ≈ 3000(1.159274)
A ≈ $3477.82
Therefore, the value of the savings account after 5 years is approximately $3477.82.