Final answer:
The balance in the account after 30 years will be approximately $7884.
Step-by-step explanation:
To calculate the balance in the account, we can use the formula for compound interest: A = P(1 + r/n)^(nt).
Where:
- A is the final balance
- P is the initial deposit
- r is the annual interest rate
- n is the number of times interest is compounded per year
- t is the number of years
To find the balance, we plug these values into the formula:
- P = $4600
- r = 1.8% or 0.018 (in decimal form)
- n = 4 (since interest is compounded quarterly)
- t = 30 years
Plugging in the values from the question, we have:
A = 4600(1 + 0.018/4)^(4*30)
Simplifying the equation gives:
A = 4600(1.0045)^(120)
A = 7884.07
The balance in the account after 30 years will be approximately $7884.