Question: A businessman wishes to earn 7% on his capital after payment of taxes. If the income from an available investment will be taxed at an average of 42%, what minimum rate of return, before the payment of taxes, must the investment offer to be justified?
This is a question under "Simple Interest" from the book I am using. The formulas I know in that topic is:
Simple Interest = (Principal Cost)(rate of interest)(number of periods)
Simple Interest = Future amount - Principal amount. Where in F = P (1 + in)
Rate of Return = [(Current value - Original Value) / (Original Value)] x 100
But I can't relate any of those formula for the problem above. The book shows no solution, just the correct answer: 12.07& Tried to search online for the solutions but no luck.
Just a clue would suffice on how to answer the problem. Any help would be appreciated. Thank you.
I always find it helps to convert the problem into words and use a convenient $100 starting sum such that the math becomes obvious. Instead of blindly guessing which standard formula to use, it helps in determining a correct formula and intuitively understanding the solution. With that.....
$\$100$ times the rate of return times $0.58$ (the amount after taxes) equals $\$7$
Here you can see why simply multiplying the two given percentages doesn't work. The quantity of interest is the amount remaining after taking out 42% in tax.
Now we can substitute the rate of return for $r$ and solve the equation.
$100r \cdot 0.58 = 7$
$100r = 12.07$
$r = .1207$ or $12.07\%$