Bond Valuation: Future Value of Ordinary Annuity

Future Value of a Special Money Plan

Introduction: Hey there! Let's talk about a cool money plan called an annuity. It's like a magic jar where money appears or disappears regularly. The future value of this annuity is like predicting how much treasure you'll have in your jar in the future. This helps grown-ups make smart choices about their money plans, like saving up or getting ready for a happy retirement.

Formula for Future Value of the Magic Jar: To unlock the magic, we have a special code, like a treasure map:

FV = P * ((1 + r)^n - 1) / r

Here's what each symbol means:

FV: Future value of all the treasure
P: How much treasure you add or take away regularly
r: How much extra treasure appears or disappears each time (we call this interest)
n: How many times you play with your treasure in total

Example: Let's say you're putting $1,000 every year into your magical jar, and every year, it grows by 6%. After 5 years, you want to peek inside and see how much treasure you've got. The magic code helps us figure it out:

FV = $1,000 * ((1 + 0.06)^5 - 1) / 0.06

So, after 5 years, your magical jar would have about $5,637.00.

First, we calculate what's inside the parentheses: (1 + 0.06)^5.
- It means you add 6% to 1 (your starting point) five times because you're playing with your jar for 5 years.
- So, it becomes (1.06)^5.
Next, we calculate the whole thing inside the square brackets: ((1.06)^5 - 1).
- This shows how much your treasure has grown over 5 years.
After that, we multiply this growth by your regular treasure addition: $1,000 * ((1.06)^5 - 1).
Finally, we divide the total by how much extra treasure appears each time (interest): $1,000 * ((1.06)^5 - 1) / 0.06.

And there you have it! After 5 years, your magical jar would have about $5,637.00.

I hope this helps! If you have any more questions or want to dive into another example, feel free to let me know!

This article takes inspiration from a lesson found in FIN 4243 at the University of Florida.