# Homework Help: Rate of return with logs [engineering economics]

1. Sep 11, 2010

### Jim01

1. The problem statement, all variables and given/known data

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?

2. Relevant 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.

3. 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.

2. Sep 11, 2010

### danago

Think about how you would invert a logarithmic function:

$$y = \log x \Leftrightarrow x = {10^y}$$

3. Sep 11, 2010

### xcvxcvvc

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