Question 100918: Hello! I am reviewing future values for my Finance class and am completely befuddled on the logical progression of the time value of money formulas. It has been quite some time since I have taken Algebra, and that is essentially why I can't figure this transformation out.
FV1 = PV + kPV
must transform into:
FV1 = PV(1+k)
I understand the basics cross-multiplying, but cannot for the life of me figure out how the former was transformed into the latter. Your assistance would be greatly appreciated!
Jonathan Pounds
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! FV1 = PV + kPV
must transform into:
FV1 = PV(1+k)
I understand the basics cross-multiplying, but cannot for the life of me figure out how the former was transformed into the latter. Your assistance would be greatly appreciated!
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Try it with numbers and you will see that it works.
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The property is called "distribution"
A statement of the property says: Multiplication distributes over addition.
Here it is in symbols: a(b+c) = ab+ac
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Your Problem:
FV1 = PV + kPV
Fv1 = PV(1+k)
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If PV = 4 and k=3
then FV! = 4+3*4 = 16
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similarly 4(1+3)= 16
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Therefore 4+3*4 = 4(1+3)
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Cheers,
Stan H.
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