Find the value after five years of a $3,000 savings account that pays 3% interest compounded yearly. Round the answer to two decimal places.(1 point) $
To find the value after five years of a savings account, we can use the formula for compound interest:
A = P (1 + r/n)^(nt)
where:
A = the future value of the investment/loan, including interest
P = the principal investment amount (the initial deposit or loan amount)
r = annual interest rate (as a decimal)
n = number of times that interest is compounded per year
t = number of years the money is invested or borrowed
In this case, the principal investment amount (P) is $3,000, the annual interest rate (r) is 3% or 0.03 as a decimal, the number of times interest is compounded per year (n) is 1 (compounded yearly), and the number of years (t) is 5.
Substituting the given 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 * 1.159274519
A ≈ 3477.82
Therefore, the value after five years of a $3,000 savings account that pays 3% interest compounded yearly is approximately $3477.82.