Final answer:
To find the final amount in a savings account with daily compounded interest after 7 months, the compound interest formula A = P(1 + r/n)^(nt) must be used, with P = $550, r = 0.0275, n = 360, and t = 7/12. After performing the calculation, the answer can be matched to the given options.
Step-by-step explanation:
The subject of this question is Mathematics, specifically it deals with compound interest. To calculate the final amount in a savings account with daily compounded interest, we use the compound interest formula: A = P(1 + r/n)^(nt), where A is the amount of money accumulated after n years, including interest, P is the principal amount (initial deposit), r is the annual interest rate (decimal), n is the number of times that interest is compounded per year, and t is the time the money is invested for in years.
In this case, we're given a principal amount (P) of $550, an annual interest rate (r) of 2.75%, which is 0.0275 in decimal form, the interest is compounded daily which means n would be 360, and t is the time in years, which since we are only working with 7 months, this would be 7/12.
The calculation would be as follows:
- Convert the annual interest rate from a percentage to a decimal by dividing by 100: r = 2.75 / 100 = 0.0275.
- Calculate the daily interest rate: daily rate = r / 360.
- Convert the investment period from months to years: t = 7 / 12.
- Substitute the values into the compound interest formula and solve for A.
After performing the calculation, we can compare the result to the options given in the question to find the correct answer.