Future Value Formula - Explained
As part of the development of my compound interest calculator, I incorporated the ability to include additional monthly deposits and deductions in calculations. In my earlier article discussing the compound interest formula, I featured a formula for the future value of a series. So, today, I thought we'd take a look at that formula in some more depth.
The future value formula (FV) allows people to work out the value of an investment at a chosen date in future, based on a series of regular deposits made up to that date (using a set interest rate). Using the formula requires that the regular payments are of the same amount each time, with the resulting value incorporating interest compounded over the term.
In this article we'll delve into the formulae available and then go through a couple of examples. At the bottom of this article you'll find an interactive formula, which will allow you to enter figures of your choosing and see how the calculation is made.
Future Value of a Series Formula
A = PMT × (((1 + r/n)^(nt) - 1) ÷ (r/n))
The formula above assumes that deposits are made at the end of each period (month, year, etc). Below is a variation for deposits made at the beginning of each period:
A = PMT × (((1 + r/n)^(nt) - 1) ÷ (r/n)) × (1+r/n)
A = the future value of the investment, including interest
PMT = the payment amount per period
r = the annual interest rate (decimal)
n = the number of compounds per period
t = the number of periods the money is invested for
Future value example 1
An investment is made with deposits of $100 per month (made at the end of each month) at an interest rate of 5%, compounded monthly (so, 12 compounds per period). The value of the investment after 10 years can be calculated as follows...
PMT = 100. r = 5/100 = 0.05 (decimal). n = 12. t = 10.
If we plug those figures into formula 1, we get:
Total = [ PMT × (((1 + r/n)^nt - 1) ÷ (r/n)) ]
Total = [ 100 × (((1 + 0.00416)^(120) - 1) ÷ (0.00416)) ]
Total = [ 100 × (0.647009497690848 ÷ 0.00416) ]
Total = [ 15528.23 ]
So, the investment figure after 10 years will stand at $15,528.23.
Future value example 2
An individual decides to invest $10,000 per year (deposited at the end of each year) at an interest rate of 6%, compounded annually. The value of the investment after 5 years can be calculated as follows...
PMT = 10000. r = 6/100 = 0.06 (decimal). n = 1. t = 5.
Total = [ PMT × (((1 + r/n)^(nt) - 1) ÷ (r/n)) ]
Total = [ 10000 × (((1 + 0.06)^5 - 1) ÷ 0.06) ]
Total = [ 10000 × (0.3382255776 ÷ 0.06) ]
Total = [ 10000 × 5.63709296 ]
Total = [ 56370.9296 ]
Our investment balance after 5 years is therefore $56,370.93. This would be comprised of $50,000 in investment and $6,370.93 in interest.
Interactive future value formula
PMT × ((( ^ ) - 1) ÷ )
Written by Alastair Hazell
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Last update: 20 December 2017
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