Final answer:
Using the compound interest formula, the final amount in the savings account after 5 years with a 4% annual interest rate and an initial deposit of $30,000 is approximately $36,482.97.
Step-by-step explanation:
To calculate the amount in the savings account after 5 years with an initial deposit of $30,000, an interest rate of 4% compounded annually, you can use the formula for compound interest: A = P(1 + r/n)^(nt). 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 (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.
Using this formula:
- P = $30,000
- r = 4/100 = 0.04
- n = 1 (since the interest is compounded annually)
- t = 5 years
So, A = 30,000(1 + 0.04/1)^(1*5) = 30,000(1 + 0.04)^5 = 30,000(1.04)^5
After calculation, A ≈ $36,482.97. Hence, at the end of 5 years, the amount in the savings account will be approximately $36,482.97.