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## Time Value of Money Part XII

### What is a Perpetuity? – Getting Paid Forever

On my first time over to England, we took a little side trip from London to visit the city of Dover. This city is known for its famous white cliffs and also has a pretty cool castle overlooking the English Channel. Let’s pretend that I was walking along the Dover beach and discovered a chest that looked like it came from an old ship. At the same time, we’ll say that an archaeologist conveniently walks by and offers me $10,000 per year for the rest of my life if I give her the chest. While this all sounds awesome, we should do a couple of quick calculations to figure out how much $10,000 per year for the rest of my life is really worth to me today. In other words, we want to calculate the present value of a perpetuity. When asked “What is a Perpetuity?” I usually answer that it is payments of a set amount of money that occur on a routine basis and continues forever (pretty much like an annuity without an end date).

While I won’t live forever, I plan to be around for a while so we’ll say that it’s close to a perpetuity. Let’s also say that I could currently save at 3% in my savings account. To figure out how much the $10,000 per year is worth to us, we can use the formula below:

Value of Perpetuity = Value of Payment / Interest Rate

All we have to do for this problem is take the $10,000 per year and divide by 3%:

Value of Perpetuity = $10,000 / 3% = $10,000 / 0.03 = $333,333.33

So the steam of $10,000 per year forever is worth $333,333.33 to me today. We’ll just say that I’d accept the deal if this really happened.

### One More Perpetuity Example to Try

To get a little more small business financial management practice, let’s say that you find out a good secret about your sibling and they promise to pay you $100 per year for the rest of your life to never reveal it. At the time you could save at 5% in your savings account. To figure out how much that is worth to you today (the present value), we can just divide the $100 by the interest rate 5% to calculate the present value of a perpetuity:

Value of Perpetuity = $100 / 0.05 = $2000

So really, it’s like you sibling is paying you $2000 to keep their little secret quiet.

**Key Takeaway: **When asked “What is a Perpetuity?” we can say that it is payments of a set amount of money that occur on a routine basis and continues forever. To calculate how much a never ending stream of payments is worth to us today, we can take the value of each payment divided by the interest rate we could get over that period.

Test Your Knowledge: What is a Perpetuity?

**To Next Lesson: ****Business Financial Statements**

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