Final answer:
Using the future value of an annuity due formula, the accumulated value of periodic $20 deposits at the beginning of every quarter for 23 years, with an interest rate of 3.42% compounded quarterly, can be calculated. It includes finding the quarterly interest rate and multiplying it with the number of deposits made over the years to use in the formula. Start saving early and use compound interest to maximize savings.
Step-by-step explanation:
To calculate the accumulated value of periodic deposits of $20 at the beginning of every quarter for 23 years with an interest rate of 3.42% compounded quarterly, we use the future value of an annuity due formula:
FV = P × { [ ( (1 + r)^n - 1 ) / r ] × (1 + r) }
Where:
- FV is the future value of the annuity
- P is the periodic deposit amount ($20)
- r is the quarterly interest rate
- n is the total number of deposits
In this case,
- The quarterly interest rate (r) is 3.42% per year, or 0.0342 annually, which divided by 4 (the number of quarters in a year) gives us 0.00855 per quarter.
- The total number of deposits (n) is 4 quarters per year multiplied by 23 years, equating to 92 deposits.
Plugging these values into the formula we get:
FV = $20 × { [ ( (1 + 0.00855)^92 - 1 ) / 0.00855 ] × (1 + 0.00855) }
After calculating, the accumulated value for the annuity due will be the future value obtained from the formula.
It's important to have all calculations verified by a financial calculator or appropriate financial software to ensure accuracy. Remember, starting to save early in life and taking advantage of the power of compound interest can significantly increase savings over time.