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Posted November 7th, 2018

Let’s Look at Compound Interest—Part 2

Last time, we looked at two concepts: compound interest and present value.

Turns out they’re two sides of the same coin. If you grasp the idea of compound interest, you also grasp the idea of present value, maybe without realizing you do.

Compound interest tells us what $1 (or $1 million) will grow to after n years if invested at a given interest rate i. $1 will grow to $(1 + i)n.  $1 million will grow to:  $1,000,000(1 + i)n.

Present value tells us what $X to be received in n years is worth today, in today’s dollars, if we assume money can be invested at a given interest rate i, which is routinely called the discount rate when talking about present value (PV).

The PV of $X dollars to be received in n years, assuming a discount rate of i, is:   $x/(1 + i)n.  The quantity (1 + i)n is called the compound interest factor.

Note what is obvious: PV is equal to the amount of money to be received at the end of n years divided by the compound interest factor corresponding to n years and i rate of interest.

This is why compound interest and present value are two sides of the same coin.

Now a homework problem the solution to which will be given next time. Here’s the problem: Your VP for development asks you to determine the present value of a $1 million bequest to be received under the will of a living individual aged 79. Question: What two assumptions do you need to make to determine the present value?

Hint: Answer the question asked, not some other question.

by Jon Tidd, Esq

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