Part A: The formula for the future value of an investment with compound interest is given by:
A = P(1 + r/n)^(nt)
Where: A = the future value of the investment P = the principal investment amount r = the annual interest rate (as a decimal) n = the number of times the interest is compounded per year t = time in years
For this situation, P = $1,500 r = 2.75% = 0.0275 (since the interest rate is given as an annual rate, we need to divide it by 100 to convert it to a decimal) n = 365 (since interest is compounded daily) t = 1 (since we are looking for the value after one year)
Therefore, the equation to model this situation is:
A = 1500(1 + 0.0275/365)^(365*1)
Part B: To find the value of the account after one year, we can simply substitute t=1 into the equation:
A = 1500(1 + 0.0275/365)^(365*1) = $1,543.21
Therefore, the amount of money in the account after 1 year is $1,543.21.
Part C: To find the value of the account after 5 years, we need to substitute t=5 into the equation:
A = 1500(1 + 0.0275/365)^(365*5) = $1,805.59
Therefore, the amount of money in the account after 5 years is $1,805.59.