# Perpetual income – What it is, definition and concept | 2023

A perpetual lease is a lease that has no expiration time. Therefore, it can be defined as an income of infinite or unlimited duration..

That is, a perpetual income is made up of a series of payments of the same amount of money that are received periodically. In addition, these payments are received for an indefinite period of time.

For that reason, its final value cannot be calculated, only its present value. Since, time extends to infinity.

## Important terms to understand perpetual income

The most important terms to understand perpetual income are:

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• The present or current value: It is the value that an amount of money that we will receive in the future has today. In perpetual income this value extends to infinity. This can be represented by VP, VA, rp and A∞.
• The capital, money or share: It is the amount of money that is received as payment of the perpetual income. can be identified with C, P, and R.
• The interest rate: It is the percentage paid for using or investing an amount of money in the financial system. It is represented with Yo.

Formulas that can be used to obtain perpetual income

Different formulas can be used to calculate perpetual income. The most used formulas are:

## Cases and examples to apply the perpetual income

### 1. Rentals

To begin with, a rent is an income that is generated by the agreed payment of an amount of money in exchange for using a movable or immovable property. This for a certain period of time.

In this example, let’s assume that we rent a building for \$15,000 per year to a multinational company. If the interest rate is 4% per year. What is the current value of the building?

Applying the formula TO∞=R/Yo we obtain:

A∞=15000/0.04 =\$375,000

The current value of the building is \$375,000.

### 2. The bonuses

On the other hand, a bond is a debt financial instrument that companies or the government use to obtain financing. So if the government offers perpetual bonds for \$20,000 and the interest rate is 5% per year. What is the present value of the bond?

Applying the formula TO∞=R/Yo we obtain:

A∞=20000/0.05 =\$400,000

The current value of the bond is \$400,000.

### 3. Preference shares

While, preferred shares are ownership titles in whole or in part of a company. Being able to generate fixed or variable income dividends. Shares that produce perpetual income are those that the issuer cannot liquidate.

If we acquire a share that produces \$200 per month. Considering that the annual interest rate is 12%. What is the present value of the stock? We must take into account that the performance of the action is per month. But, the interest rate is 12% per year, so the rate will need to be divided over 12 months. Giving a monthly interest rate of 1%.

Applying the formula TO∞=R/Yo we obtain:

A∞=200/0.01 =\$20,000

The current value of the stock is \$20,000.

### 4. Fixed-term deposits

Now, a fixed-term deposit is when the account holder deposits a certain amount of money and the bank offers an interest rate return for a certain time. In order for it to work as a perpetual income instrument, the depositor only withdraws the interest, but keeps the principal of the deposit intact.

For example, if a person makes a deposit that produces an income of \$35,500 per year, if the interest rate is 5%. What is the present value of this deposit?

Applying the formula TO∞=R/Yo we obtain:

A∞=35,500/0.05 =\$710,000

The current value of the deposit is \$710,000.