need help to explain to kids

[rsis]

What is the best way to show a 13 year old the difference between an Internal Rate of Return and a compounded return.

 

[JeffM]

What is the best way to show a 13 year old the difference between an Internal Rate of Return and a compounded return.

I have no idea why any 13 year old needs to know this distinction.

EDIT: I have just seen Halls of Ivy's post below mine. If indeed you are trying to explain the difference between simple interest and compound interest, something which a 13 year old should understand, then you can ignore this post. I should have thought to ask for clarification of your question.

The basic idea of the internal rate of return is this

\(\displaystyle V = \displaystyle \sum_{i=0}^n\left(\dfrac{C_i}{(1 + r)^i}\right),\ where\)

V = present value of an investment,

C₀ = initial cash flow (with expenditures and receipts given opposite signs)

C_i = cash flow at end of period i,

n = number of periods, and

r = measure of time preference (or interest).

This basically says that the longer you have to wait to get a given amount of money back, the less desirable the investment is. You do not want to make an investment with a negative value so, given the cash flows and the number of periods, the question reduces to what rate ensures that the value is NOT negative. If the value is not negative, it is certainly at least zero. So we change our equation to read

\(\displaystyle 0 \le \displaystyle \sum_{i=0}^n\left(\dfrac{C_i}{(1 + r)^i}\right).\)

When we solve that inequation for r, we get the internal rate of return. It is just a solution to an inequation that says at what value of interest (or time preference) a given investment will not have a negative present value. With me so far?

Solving this inequation can be very ugly if cash flows are quite irregular, and the term "internal rate of return" is used by people who have to deal with such complex situations. If, however, the cash flows are very regular, solving the inequation is much easier, and people who deal with that sort of situation use the term "compounded rate of return." Fundamentally, it is the same concept, with a different term used by people who work on problems of differing complexity.

 

[HallsofIvy]

If you mean the difference beween "simple interest" and "compound interest". With simple interest, we calculate the interest, Initial amount times annual interest rate times number of years. If this was a loan, you would pay the initial amount and interest at the end of the loan term.

With compound interest, we calcuate the interest, as with simple interest, for the specified time interval (month, quarter year, year) but instead of paying it, you add the interest on to the principle and extend to the next term.