# Future value

The future value (VF) is the value that a certain amount of money will have in the future that we currently maintain or that we decide to invest in a certain project.

The future value (VF) allows us to calculate how the value of the money that we currently have (today) will change considering the different investment alternatives that we have available. In order to calculate the VF we need to know the value of our money is the current moment and the interest rate that will be applied in the coming periods.

The concept of future value is related to that of Present Value, the latter reflects the value that a flow of money would have today that we will receive in the future.

Future Value is used to evaluate the best alternative as to what to do with our money today. Also to see how the value of money changes in the future.

## Future value concept

The concept of future value seeks to reflect that if we decide to delay our current consumption it will be for a prize, something worthwhile. In this way, we expect the future value to be greater than the present value of an amount of money that we currently have since a certain interest rate or profitability is applied to it . For example, if today I decide to save money in a bank savings account, this amount of money will grow at the interest rate that the bank offers me.

## Relationship between present value and future value

They are two sides of the same coin. Both reflect the value of the same money at different points in time. It is always better to have the money today, rather than waiting, unless we are paid interest on it. In the future value formula we can clear the present value and vice versa.

## Future value formula

The formula for calculating future value depends on whether the interest that is applied is simple or compound.

• Simple Interest Formula

It occurs when the interest rate is applied only on the principal or initial amount, not on the interest that is earned over time. The formula is as follows:

VF = VP x (1 + rxn)

Where:

VF = future value

PV = present value (the amount we invest today to earn interest)

r = simple interest rate

n = number of periods

Example: Suppose you invest 1000 euros in a savings account that offers a simple interest rate of 10%. What is the future value in the next two years?

VF = 1000 x (1 + 10% x 2) = 1200 euros (interest earned is 200)

• Compound Interest Formula

In this case, the interest rate is applied on the initial amount and also on the interest that is earned each period. The formula is as follows:

VF = VP x (1 + r) n

## Example of how to calculate future value

Example: Suppose the Bank now offers you a compound interest rate of 10% on savings. What is the future value in the next two years?

VF = 1000 x (1 + 10%) 2 = 1210 euros

This implies that the interest earned is 210, the first year the interest is 10% of 1000 (100 euros), the second year as long as it is 10% of 1100 (110 euros).