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## Time Value of Money Explained Part III

**Calculating Present Value to Get to the Country of Kilts and Golf**

As I was going through college, my first opportunity to travel overseas took me to the country of Scotland. While my cousin was studying abroad in Edinburgh, he found a great deal switching cable companies and got me a free ticket to fly over. Although my ticket was free, I still needed to save what I projected to be about $1000 for the rest of the trip. Since it was about a year out, I needed to figure out how much I had to save at that time so I would have the $1000 available when it was time to get on the plane. To figure out this problem, we’ll work through calculating present value of the $1000 in the future.

Essentially, when someone talks about the present value, they are talking about how much money we would need to invest now to have a certain amount in the future. In this case, I needed to find how much I would have to save today to have $1000 in one year.

For this problem, let’s assume that I could invest in a savings account that gave me 5% interest. To calculate the total that I would have to save today, I have to divide by the interest rate that I could get plus 1:

$1000 / (1+5%) = $1000 / (1 + 0.05) = $1000 / 1.05 = $952.38

So if I want to have exactly $1000 by the time I step on the plane to go to Scotland in one year, I need to invest $952.38 today at 5% interest. Therefore, the present value of $1000 one year in the future is $952.38 if I can invest at a 5% interest rate.

**Heighten my Interest Calculating Present Value in Another Example**

Taking my savings plan to get to Scotland as another example, let’s say that I could invest at 7% instead of 5%. To make sure that I had $1000 in one year, I’d have to invest the following amount at 7%:

$1000 / (1+7%) = $1000 / (1+0.07) = $1000 / 1.07 = $934.58

As the interest rate that I could get increased in the savings account, the amount that we would have to invest decreased. This makes sense since we’ll be able to get more interest on what I initially invested at a higher interest rate. What this shows is that as the interest rate increases, the present value of money in the future decreases.

**Calculating Present Value – Another Small Business Financial Management Example**

Let’s go through one more example to make sure we understand the concept of the present value. Say that we wanted to save a total of $35,000 in a year for a house down payment in that nice neighborhood across town. If we were able to save at 3%, how much would we have to invest today to have $35,000 one year from now?

When calculating present value, we need to divide the amount we want to have by 1 plus the interest rate:

$35,000 / (1 + 3%) = $35,000 / (1 + 0.03) = $35,000 / 1.03 = $33,980.58

So, this means that we’ll have to invest $33,980.58 in our 3% savings account today if we want to have $35,000 in one year. Said another way, the present value of $35,000 one year from now is $33,980.58 if the interest rate is 3%.

**Key Takeaway: **Calculating present value is finding the amount of money that we would have to invest today to have a certain amount of money in the future. For the next lesson, we’ll see how the present value and the future value can be used to calculate each other.

Test Your Knowledge: Calculating Present Value

**To Next Lesson: Future Value Versus Present **

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