An annuity due involves making payments at the beginning of each period, and its future value is determined by four key entities: periodic payment, interest rate, number of periods, and present value. The present value represents the current worth of the annuity’s future payments, while the interest rate determines the rate at which the value grows over time. The number of periods signifies the duration of the annuity, and each payment made at the beginning of a period contributes to the future value calculation.
The Best Structure for Future Value of Annuity Due
Calculating the future value of an annuity due requires determining the present value of each due payment and then summing them up to obtain the total future value. Let’s look at the steps:
1. Identify the Input Variables:
- P: The principal or present value of each payment
- r: The annual interest rate
- n: The number of periods
2. Calculate the Future Value of Each Due Payment:
- Future Value of Due Payment = P * (1 + r)^n
3. Summing Up the Future Values:
- Future Value of Annuity Due = Σ [P * (1 + r)^n]
This formula calculates the future value of annuity due, where the payments are made at the beginning of each period.
Example:
Consider an annuity due with the following parameters:
- P = $1,000
- r = 5% per year
- n = 5 years
Step 1: Calculate the future value of each due payment:
- Future Value of Due Payment = $1,000 * (1 + 0.05)^5 = $1,276.28
Step 2: Sum up the future values:
- Future Value of Annuity Due = $1,276.28 + $1,276.28 + $1,276.28 + $1,276.28 + $1,276.28 = $6,381.40
Therefore, the total future value of this annuity due is $6,381.40.
Table Summarizing the Calculation:
| Period | Present Value | Future Value |
|---|---|---|
| 1 | $1,000 | $1,276.28 |
| 2 | $1,000 | $1,276.28 |
| 3 | $1,000 | $1,276.28 |
| 4 | $1,000 | $1,276.28 |
| 5 | $1,000 | $1,276.28 |
| Total | $5,000 | $6,381.40 |
Question 1:
What is the concept of future value of annuity due?
Answer:
Future value of annuity due is the total value of a series of periodic payments made at the end of each period, which are invested at a specified interest rate for a specified number of periods.
Question 2:
How is future value of annuity due calculated?
Answer:
Future value of annuity due is calculated using the formula: FV = P * [(1 + r)^n – 1] * (1 + r), where P is the periodic payment, r is the interest rate, and n is the number of periods.
Question 3:
What are the key factors that influence future value of annuity due?
Answer:
The key factors that influence future value of annuity due are: the amount of each periodic payment, the interest rate, the number of periods, and the timing of the payments (due at the end of each period).
And that’s a wrap, folks! I hope this quick dive into the future value of an annuity due has been helpful. Remember, it’s all about figuring out how much your future income stream is worth today. If you’ve got any more financial puzzles that need solving, don’t hesitate to drop by again. I’ll be here, ready to guide you through the maze of money matters. Take care and stay prosperous!