Final answer:
The accumulated value of periodic deposits into an investment fund can be calculated using the compound interest formula. Plugging in the given values, the accumulated value after 5 years is approximately $34,859.54.
Step-by-step explanation:
To calculate the accumulated value of periodic deposits, also known as compound interest, we can use the formula:
A = P(1 + r/n)^(nt) - P
Where:
- A is the accumulated value
- P is the periodic deposit amount
- r is the annual interest rate (as a decimal)
- n is the number of compounding periods per year
- t is the number of years
In this case, the periodic deposit amount is $6,000, the annual interest rate is 3.50% (0.035 as a decimal), the compounding period is quarterly (n = 4), and the number of years is 5. Plugging these values into the formula, we get:
A = $6,000 * (1 + 0.035/4)^(4*5) - $6,000
Simplifying the equation gives us:
A = $6,000 * (1.00875)^(20) - $6,000
Calculating the expression inside the parentheses and multiplying it by $6,000, we find that the accumulated value is approximately $34,859.54.