## Calculations for compounding and discounting

If you have a sum of money today (Present Value) and you want to determine how much it would be worth in the future (Future Value), you can use the formula below.

### The Compounding Formula

[math] FV = PV (1 + i)^t [/math]

Where:

- FV is Future Value
- PV is Present Value
*i*is a specified interest rate (in decimal form), and*t*is the amount of time

Using the example given in my previous post on Time Value of Money (TVM), I will show you how to use this calculation.

If you have $907 today and you can earn 5% interest per year, how much will this sum be worth in 2 years time?

- PV is $907
*i*is 0.05 (5% in decimal form – divide by 100 to get this)*t*is 2 (number of years)

Note that you need to make sure that the interest rate used corresponds to the same time period (in this case annually). If you were compounding monthly, then you’d need to adjust the interest rate to the monthly rate.

[math] FV = 907 (1 + 0.05)^2 [/math]

[math] FV = 907(1.1025) [/math]

[math] FV = 999.97 [/math]

If you have $613 today and you can earn 5% interest per year, how much will this sum be worth in 10 years time?

[math] FV = 613 (1 + 0.05)^{10} [/math]

[math] FV = 613(1.63) [/math]

[math] FV = 999.19 [/math]

### The Discounting Formula

If you have an expectation of a certain value at a future date, then you can discount this Future Value back to today’s Present Value to determine what something is worth to you today. This formula is commonly used when valuing businesses and commercial property.

[math] PV = \frac{FV} {(1 + i)^t} [/math]

Example:

If you expect to have $1,000,000 in 11 years time and the current interest rate is 5%, how much would you expect to put away today (in a lump sum) to achieve this?

Or, (same numbers, but different question) how much would you pay today for a building that you expected to be worth $1,000,000 in 11 years time?

- FV is $1,000,000
*i*is 0.05 (5% annual interest in decimal form)*t*is 11 (number of years)

[math] PV = \frac{1000000} {(1 + 0.05)^{11}} [/math]

[math] PV = \frac{1000000} {1.71034} [/math]

[math] PV = $584,679 [/math]

Another example, as mentioned in my previous post.

If you expect to have $1,000,000 in retirement savings in 11 years and the inflation rate is 3% per annum, how much spending power will you have?

[math] PV = \frac{1000000} {(1 + 0.03)^{11}} [/math]

[math] PV = \frac{1000000} {1.384} [/math]

[math] PV = $722,421 [/math]

So if you plan on being a “millionaire” in 11 years time, you’ll only have the wealth of someone who has $722,421 today.

Worth thinking about, isn’t it?