Rate of return with logs [engineering economics]

In summary, the conversation discusses the purchase and sale of a Picasso painting and poses a question about the return on investment. The single payment compound interest formula is suggested as a solution, but the individual is unsure how to isolate the interest rate variable. They consider using the inverse of a logarithmic function, but are unsure if it is accurate.
  • #1
Jim01
36
0

Homework Statement



In 1903, a Picasso painting was purchased for $600. The family of the original owner sold the painting in 1995 for $29,152,000. What rate of return (interest) did the family receive on the investment?

Homework Equations



Single Payment Compound Interest Formula:

F = P(1+i)n

where,

F= a future some of money (future value)
P= a present sum of money
n= number of interest periods
i = interest rate per interest period.

The Attempt at a Solution



solve for i:

F = P(1+i)n
F/P = (1+i)n
log(F/P) = n log (1+i)

This is as far as I get. I know that n log (1+i) does not equal n log 1 + n log i, but I don't know what to do to isolate the i. I can't just divide both sides by n log because there is no such thing as n log. I thought about moving n log (1+i) to the left side and setting the equation to zero, but I didn't get anywhere with that either.
 
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  • #2
Think about how you would invert a logarithmic function:

[tex]y = \log x \Leftrightarrow x = {10^y}[/tex]
 
  • #3
get rid of the power of n by raising both sides by 1/n. i don't think that log trick you're pulling is even accurate
 

FAQ: Rate of return with logs [engineering economics]

1. What is the purpose of using logs in engineering economics?

Using logs in engineering economics helps to simplify and standardize calculations involving large numbers. It also allows for easier interpretation of data and comparison of different projects or investments.

2. How is the rate of return calculated using logs?

The rate of return using logs is calculated by taking the difference between the beginning and ending log values and dividing it by the beginning log value. The result is then multiplied by 100 to express it as a percentage.

3. Can logs be used to calculate the rate of return for any type of investment?

Yes, logs can be used to calculate the rate of return for any type of investment, as long as the initial and final values are known and can be expressed as a logarithm.

4. Is there a specific base for the logarithm used in engineering economics?

In engineering economics, the most commonly used logarithm is the natural logarithm with a base of e. However, other bases such as 10 or 2 can also be used depending on the preference of the engineer or the specific application.

5. How does using logs affect the accuracy of the rate of return calculation?

Using logs can improve the accuracy of the rate of return calculation, especially when dealing with large numbers. This is because logs compress the scale of the numbers, making it easier to compare and calculate accurately. However, rounding errors can still occur, so it is important to use precise values when using logs in calculations.

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