In economy it’s important to know about future values, as the value of money changes over time. $
Theory
When we talk about future values, we are describing how much money will be worth some time in the future. Future values are often related to saving and repayment of loans, and has a quotient
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The future value
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where
Example 1
Given that you deposit
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When we’re looking at installments and savings, it’s often smart to draw timelines. A timeline helps you keep control of how many periods of time give you interest on your money. Here is an example of future values connected to saving.
Example 2
How much money will you have in the bank if you save
For this type of exercises it is a good idea to use timelines. But first we need to find out how much money you will save each year:
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Then the timeline looks like this:
This gives you the geometric series
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which is quite amazing!
Example 3
You created a bank account on 01.01.2015 with an interest rate of
Part 1 – You want to save a total of
This gives you the geometric series
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Where
The final sum is set to be
This equation can be input into a digital tool like CAS
in GeoGebra
. That will give you the solution
Part 2 – You would like to achieve the total sum of
This can be expressed as the geometric series
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This time the unknown is the annual deposit
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You can solve this equation with a digital tool, which will give you that the annual deposit has to be $