Financial Algorithms Cookbook | Time Value of Money

Algorithm: Calculating the Present Value

Typical Uses

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Ingredients

To calculate the number of compounding periods you will need the following:

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newton_raphson?

def derivative(i, PV, FV, PMT, n, inAdv=False, continious=False):
    nFractionPart,nIntegerPart  = modf(n)
    discount = pow(1.0+i, -nIntegerPart)
    if inAdv:
        PMT *=(1.0+i)
    if continious:
        pvs =pow((1.0+i),nFractionPart) 
    else:
        pvs =(1.0+ i*nFractionPart)
    return PV + ( PMT*((1-discount)/i) + FV*discount)/pvs

def interestRate(estimate, PV, FV, PMT, n, inAdv=False, continous=False):
   stop = PV
   return  100* newton_raphson(derivative,  estimate, PV, FV, PMT, n)

Example

You want to save for your childs collage bills estimated to be 100,000. She will graduate form high school in 8 years time. What annual interest rate will you need to achieve this amount on an investment of 60,000 with quarterly compounding?

FV= 100000
PV=-60000
PMT=0
n=8*4
estimate = 1.2/n
interestRate(estimate/100, PV, FV, n)
>> 1.61

So the annual interest rate is 6.44

References

• Gallager, T; Andrew Jr., J., Financial Management: Principals and Practices, Upper Saddle River, NJ: Prentice Hall, 1996
• HP-12C Business Calculator Owner's Manual, Hewlett Packard, 1984
• HP-10B Business Calculator Owner's Manual, Hewlett Packard, 1994