Explanation:
a. To calculate how much Britney will have in her account at the end of one year, we need to use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A = the final amount in the account
P = the principal amount (the initial investment)
r = the annual interest rate (as a decimal)
n = the number of times the interest is compounded per year
t = the number of years
In this case, Britney's principal amount is $4,000, the annual interest rate is 3.4% (or 0.034 as a decimal), the interest is compounded monthly (so n = 12), and the time period is 1 year (so t = 1).
Plugging in these values into the formula, we get:
A = 4000(1 + 0.034/12)^(12*1)
Calculating this expression, Britney will have approximately $4,124.63 in her account at the end of one year.
b. The Annual Percentage Yield (APY) takes into account the effect of compounding on the interest rate. To calculate the APY, we can use the formula:
APY = (1 + r/n)^n - 1
Where:
r = the annual interest rate (as a decimal)
n = the number of times the interest is compounded per year
In this case, the annual interest rate is 3.4% (or 0.034 as a decimal), and the interest is compounded monthly (so n = 12).
Plugging in these values into the formula, we get:
APY = (1 + 0.034/12)^12 - 1
Calculating this expression, the APY for Britney's account is approximately 3.412%. Rounded to the nearest thousandth of a percent, the APY is 3.412%.