# Present value of a single deposit, compounded continuously

## How do you find it?

Keep in mind that present value is the opposite of future value.

## In this video we’re looking at how to find the present value of a one-time deposit, when interest is compounded continuously.

0:28 // What is a single deposit? What does present value mean? What does compounded continuously mean?
1:34 // Future value formula and present value formula
2:49 // Overview of the example problem
3:28 // Writing down what we know
4:33 // Plugging everything into the formula
5:30 // How to interpret the answer
6:16 // Using the future value formula to find present value

Keep in mind that present value is the opposite of future value. Future value is how much we need to have at some point in the future; present value is how much we need to have right now.

Single deposit, or one-time deposit, means that we’re depositing money into an account once, and then not adding any more to it or taking any amount away from it. So we make one deposit one time, and then don’t touch it. That’s different than an income stream problem, where we might make regular deposits every month, or every year, or make regular withdrawals.

Compounded continuously, or continuously compounded interest, is when interest is being compounded constantly into the principal balance. That’s in contrast to interest that’s compounded a certain number of times per year, like every year, every quarter, or every month. We use certain formulas with continuously compounded interest, and a totally different set of formulas for interest compounded a certain number of times per year.

To find the present value of a single deposit when interest is compounded continuously, we need to know the future value that we want, the interest rate, and the time between now and when we want to reach the future value amount. For example, if we know we want \$10,000 in our account in 5 years, and we know the account pays 7% interest compounded continuously, then we’ll be able to use our formula to find the present value amount that we need to have today in order to get there.

## Want to learn more about Applications of Integrals? I have a step-by-step course for that. 😃

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