Time Value of Money

Summary

• Money has value over time
• Evaluating future costs and benefits now needs to consider time value of money

Interest and Interest Rates

• Lending money should be compensated
• Since the lenders loose the opportunity to invest the money they rent out, they should get additional compensation so it acts in the same way
• Therefore, the compensation of loaning money is the interest payment
• I.e instead of rent for an apartment, we charge interest

This can be represented as…
$F=P+I=P+Pi=P\left(1+i\right)$

• $i$ → interest rate
• $P$ → present worth
• F → future worth of P

Alternatively, over n years your interest can…
compound (using the Compound Effect)
$F=P{\left(1+i\right)}^n$
or be simple

$F=P\left(1+in\right)$

Simple Interest Rate

Not compounding, interest amounts are not considered for calculating interest in the future (the initial value is called the principle investment)

You can find the compound interest amount through $I_C=F-P$