Final answer:
To determine the final amount in an account with quarterly compounded interest after one year, we use the compound interest formula A = P(1 + r/n)^(nt). With a principal of $3100, an annual rate of 3.2%, quarterly compounding, and a time span of 1 year, the amount is approximately $3199.42.
Step-by-step explanation:
To calculate the amount of money in an account after one year with quarterly compounded interest, we can use the formula for compound interest, which is A = P(1 + r/n)^(nt), where:
A is the amount of money accumulated after n years, including interest.
P is the principal amount (the initial amount of money).
r is the annual interest rate (decimal).
n is the number of times that interest is compounded per year.
t is the time the money is invested for, in years.
In this case:
P = $3100
r = 3.2% or 0.032
n = 4 (since the interest is compounded quarterly)
t = 1 year
Now substituting the values into the formula, we get:
A = 3100(1 + 0.032/4)^(4*1)
First, we calculate 0.032/4 which is 0.008 and then add 1 to it, getting 1.008. Next, we raise this sum to the power of 4 because the interest is compounded quarterly for 1 year and then multiply it by the principal amount:
A = 3100(1.008)^4
Finally, calculating the power and then the product:
A = 3100 * 1.032328 (approximately)
A ≈ $3199.42
So, after one year, the money in the account, with interest compounded quarterly, is approximately $3199.42.