(a) To find the amount in the account at the end of 1 year, we use the formula:
A = P(1 + r)^n
where A is the amount in the account at the end of the year, P is the principal (the initial amount deposited), r is the interest rate as a decimal, and n is the number of times the interest is compounded in a year. In this case, P = $4500, r = 0.06 (since the interest rate is 6%), and n = 1 (since the interest is compounded once a year). So, we have:
A = $4500(1 + 0.06)^1
= $4500(1.06)
= $4770
Therefore, the amount in the account at the end of 1 year is $4770.
(b) To find the amount in the account at the end of 2 years, we again use the formula:
A = P(1 + r)^n
However, in this case, n = 2 (since the interest is compounded twice in 2 years). So, we have:
A = $4500(1 + 0.06)^2
= $4500(1.1236)
= $5061.20
Therefore, the amount in the account at the end of 2 years is $5061.20.