Calculating Future Value of an Ordinary Annuity and Total Interest Earned
Understanding the future value of an ordinary annuity and the total interest earned is crucial for personal finance and investment planning. This article will guide you through the process using a practical example. We'll calculate the future value of an ordinary annuity with annual payments of P1000 and an annual interest rate of 4%, over a period of three years. This involves using the future value of annuity formula and breaking down the total interest earned.
What is an Ordinary Annuity?
An ordinary annuity is a series of equal payments made at the end of each period. In this context, we are looking at a series of payments, P1000, made at the end of each year for three years, with an annual interest rate of 4%. This type of annuity is commonly used in financial planning, retirement savings, and investment calculations.
Future Value of Annuity Formula
The formula to calculate the future value of an ordinary annuity is as follows:
FV P times frac{(1 r)^n - 1}{r}
Where:
FV Future value of the annuity P Annual payment (P1000) r Annual interest rate (0.04) n Number of years (3)Step-by-Step Calculation
Step 1: Calculate the Future Value
Substitute the given values into the formula to calculate the future value:
FV 1000 times frac{(1 0.04)^3 - 1}{0.04}
Calculating the components:
1. Calculate (1 r)^n
(1 0.04)^3 1.124864
2. Calculate (1 r)^n - 1
1.124864 - 1 0.124864
3. Divide the result by r
frac{0.124864}{0.04} 3.1216
4. Multiply by P
1000 times 3.1216 3121.60
Therefore, the future value of the annuity after three years is P3121.60
Step 2: Calculate Total Payments and Total Interest Earned
Total Payments P times n 1000 times 3 3000
To find the total interest earned, subtract the total payments from the future value:
Total Interest Earned Future Value - Total Payments 3121.60 - 3000 121.60
Summary
Here's a summary of the calculations:
Future Value of the Annuity: P3121.60 Total Interest Earned: P121.60Conclusion
Understanding and calculating the future value of an ordinary annuity and the total interest earned can be valuable for financial planning. This example demonstrates how to apply the future value of annuity formula and provides a practical insight into the concept.