Final answer:
The amount in the account at the end of 1 year would be $4770, and at the end of 2 years would be $5058.20, based on a 6% interest rate compounded annually from an initial deposit of $4500.
Step-by-step explanation:
The student's question pertains to the calculation of compound interest for an initial deposit made in a bank account.
(a) To find the amount in the account at the end of 1 year, we use the formula for compound interest:
A = P(1 + r/n)^(n*t)
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 (in decimal).
- n is the number of times that interest is compounded per year.
- t is the time the money is invested for in years.
Given that P = $4500, r = 0.06 (since 6% = 0.06), n = 1 (compounded once a year), and t = 1, we find that:
A = 4500(1 + 0.06/1)^(1*1)
A = 4500(1 + 0.06)
A = 4500(1.06)
A = $4770 at the end of 1 year.
(b) To find the amount in the account at the end of 2 years:
A = 4500(1 + 0.06/1)^(1*2)
A = 4500(1 + 0.06)^2
A = 4500(1.06)^2
A = $5058.20 at the end of 2 years.