Future Value of Ordinary Annuity Calculator

What is a Future Value of Ordinary Annuity?

The Future Value of Ordinary Annuity (FVA) is a financial concept that calculates the total value of a series of equal payments made at regular intervals over a specified period, assuming a constant interest rate. This calculation is crucial for various financial planning scenarios, such as retirement savings, investment strategies, and loan repayments.

Formula for Future Value of Ordinary Annuity

The formula for calculating the Future Value of Ordinary Annuity is:

\[FV = PMT \times \frac{(1 + r)^n - 1}{r}\]

Where:

• FV = Future Value
• PMT = Regular Payment Amount
• r = Periodic Interest Rate (Annual Rate / Number of Periods per Year)
• n = Total Number of Periods

Calculation Steps

1. Determine the periodic interest rate by dividing the annual rate by the number of compounding periods per year.
2. Calculate the total number of periods by multiplying the number of years by the number of payments per year.
3. Apply the formula to calculate the future value.
4. Calculate the total payments made by multiplying the regular payment by the number of periods.
5. Determine the interest earned by subtracting the total payments from the future value.

Example

Let's consider a scenario with the following details:

• Regular Payment: $1,000
• Annual Interest Rate: 5%
• Investment Period: 10 years
• Compounding Frequency: Monthly (12 times per year)

Calculation:

1. Periodic interest rate: 5% / 12 = 0.4167% per month
2. Total number of periods: 10 × 12 = 120 months
3. Future Value: $156,657.97
4. Total payments: $120,000
5. Interest earned: $36,657.97

In this example, an individual investing $1,000 monthly for 10 years at a 5% annual interest rate, compounded monthly, would accumulate $156,657.97. This total comprises $120,000 in payments and $36,657.97 in interest earned.