# What is perpetuity formula in Finance?

The concept of perpetuity is used to describe a stream of payments that continues indefinitely into the future. The perpetuity formula is a mathematical expression used to calculate the present value of an infinite series of future payments that are expected to continue indefinitely.

To understand the formula, it’s helpful to know a few key terms:

• Present value: This refers to the value of a payment or series of payments today, as opposed to at some point in the future.
• Future value: This refers to the value of a payment or series of payments at some point in the future.
• Discount rate: This is the rate at which the present value of a payment or series of payments is reduced. It reflects the time value of money, which means that a payment received in the future is worth less than the same payment received today.

The perpetuity formula is as follows:

Present value = Payment / Discount rate

For example, let’s say you are considering an investment that will pay you \$100 per year indefinitely. If the discount rate is 5%, the present value of this investment would be calculated as follows:

Present value = \$100 / 0.05 = \$2000

This means that, if you were to receive \$100 per year indefinitely, the present value of those payments today would be \$2000.

## How the perpetuity Formula Works & how it’s Different from Annuities and Earnouts?

Perpetuities are a type of financial instrument that involve a stream of payments that continues indefinitely into the future. The perpetuity formula is a mathematical expression used to calculate the present value of an infinite series of future payments.

Here’s how the formula works:

• The payment is the amount of money that will be received at regular intervals (for example, annually or monthly)
• The discount rate is the rate at which the present value of a payment or series of payments is reduced. It reflects the time value of money, which means that a payment received in the future is worth less than the same payment received today.

Using the formula, the present value of an infinite series of payments can be calculated by dividing the payment by the discount rate.

For example, let’s say you are considering an investment that will pay you \$100 per year indefinitely. If the discount rate is 5%, the present value of this investment would be calculated as follows:

Present value = \$100 / 0.05 = \$2000

This means that, if you were to receive \$100 per year indefinitely, the present value of those payments today would be \$2000.

Perpetuities are different from annuities and earnouts in a few key ways:

• Annuities: An annuity is a financial product that involves a series of payments made at regular intervals (such as monthly or annually) over a fixed period of time. The payments may be made by an individual or an institution, such as an insurance company.
• Earnouts: An earnout is a provision in a contract that allows a seller to receive additional payments based on the future performance of a business or asset that has been sold. The payments are typically made over a fixed period of time and are contingent on the business meeting certain performance targets.

## Real world examples how to calculate with perpetuity formula

The perpetuity formula is a mathematical expression used to calculate the present value of an infinite series of future payments that are expected to continue indefinitely. Here’s an example of how the formula can be applied in the real world:

Imagine you are considering investing in a bond that pays \$100 in annual interest payments indefinitely. To determine the present value of this investment, you can use the perpetuity formula as follows:

Present value = Payment / Discount rate

Let’s say the discount rate for this investment is 5%. The present value of the bond would be calculated as follows:

Present value = \$100 / 0.05 = \$2000

This means that, if you were to receive \$100 in annual interest payments indefinitely, the present value of those payments today would be \$2000.

Here’s another example:

Imagine you are considering investing in a rental property that generates \$1,000 in monthly rental income indefinitely. To determine the present value of this investment, you can use the perpetuity formula as follows:

Present value = Payment / Discount rate

Let’s say the discount rate for this investment is 8%. The present value of the rental property would be calculated as follows:

Present value = \$1,000 / 0.08 = \$12,500

This means that, if you were to receive \$1,000 in monthly rental income indefinitely, the present value of those payments today would be \$12,500.

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