Jim opened an account with $400. The account pays three percent quarterly. How much is in the account at the end of two years? Round to the nearest dollar.
what is
400(1.03)^2 ?
To find the amount in the account at the end of two years, we need to calculate the interest earned and add it to the initial amount.
First, let's calculate the interest earned in each quarter. The account pays three percent quarterly, so the quarterly interest rate is 3% divided by 100, which is 0.03.
Next, we will use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A is the final amount
P is the principal amount (initial deposit)
r is the annual interest rate (expressed as a decimal)
n is the number of times that interest is compounded per year
t is the number of years
In this case:
P = $400
r = 0.03 (3%)
n = 4 (quarterly)
t = 2 (two years)
Now we can substitute these values into the formula:
A = 400(1 + 0.03/4)^(4*2)
Let's calculate the inside part of the parentheses first:
(1 + 0.03/4) = 1.0075
Now we substitute this value into the formula:
A = 400 * (1.0075)^(8)
Calculating this expression:
A ≈ 400 * 1.061717394
A ≈ 424.68
Therefore, the amount in the account at the end of two years will be approximately $424.68.
Rounding this to the nearest dollar, the final amount in the account will be $425.