Final answer:
To find out the amount in the fund immediately after the 30th deposit, you need to use the formula for compound interest. Based on the given information, the amount in the fund will be approximately $25,952.87.
Step-by-step explanation:
To find out how much will be in the fund immediately after the 30th deposit, we need to use the formula for compound interest. The formula is:
A = P(1 + r/n)^(nt)
Where:
- A is the amount of money accumulated after the time specified
- P is the principal amount (the initial deposit)
- r is the annual interest rate (as a decimal)
- n is the number of times that interest is compounded per year
- t is the number of years
In this case, the principal (P) is $8,000 and the annual interest rate (r) is 6%. The number of times interest is compounded per year (n) is 1, as it is compounded annually. The number of years (t) is 30. Plugging these values into the formula:
A = 8000(1 + 0.06/1)^(1*30)
Simplifying the equation:
A = 8000(1.06)^30
Using a calculator:
A ≈ $25,952.87
Therefore, the amount in the fund immediately after the 30th deposit will be approximately $25,952.87.