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Posted November 19th, 2018

Let’s Look at Compound Interest—Part 3

Last time, we left off with a homework problem.

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?

Answer: You need to assume [1] a discount rate (i), and [2] the number of years (n) your organization has to wait to receive the bequest.

These assumptions are key.

I’ll assume three discount rates (.04, .05, .06) and three waiting times (5, 10, and 15 years). These assumptions are arbitrary and are made simply for sake of illustration.

Here’s TABLE I, showing the compound interest factor corresponding to each pair of assumptions:

TABLE I

COMPOUND INTEREST FACTORS

WAIT TIME 5 Years 10 Years 15 Years
DISCOUNT RATE
.04 1.2167 1.4802 1.8009
.05 1.2763 1.6289 2.0789
.06 1.3382 1.7908 2.3966

 

Here’s TABLE II, showing the corresponding present values:

TABLE II

PRESENT VALUES ($ SIGN OMITTED)

WAIT TIME 5 Years 10 Years 15 Years
DISCOUNT RATE
.04 821,927 675,564 555,265
.05 783,526 613,913 481,017
.06 747,258 558,395 417,265

 

These tables are useful, because there’s no single “correct answer” here. It’s apparent, though, that the shorter the projected wait time and the lower the assumed discount rate, the higher the present value.

by Jon Tidd, Esq

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