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25%
2.88
3.11
30%
2.40
2.64
The Rule of 72 also works in reverse. For example, if you want to double your money in six years, divide 6 into 72;
you'll discover that you need to find an investment that pays an annual interest rate of about 12%.
Present value of a series of payments
The example in this section computes the present value of a series of future receipts, sometimes called an annu-
ity.
A man gets lucky and wins the \$1,000,000 jackpot in the state lottery. Lottery officials offer a choice:
• Receive the \$1 million as 20 annual payments of \$50,000
• In lieu of the \$1 million, receive an immediate lump sum of \$500,000
Ignoring tax implications, which is the better offer? In other words, what's the present value of 20 years of an-
nual \$50,000 payments? And is the present value greater than the single lump sum payment of \$500,000 (which
has a present value of \$500,000)?
The answer depends on making a prediction: If Mr. Lucky invests the money, what interest rate can be expec-
ted?
Assuming an expected 6% return on investment, calculate the present value of 20 annual \$50,000 payments us-
ing this formula:
=PV(6%,20,50000,0,1)
The result is -\$573,496.
The present value is negative because it represents the amount Mr. Lucky would have
to pay today to get those 20 years of payments at the stated interest rate. For this ex-
ample, we can ignore the negative sign and treat it as positive value to be compared
with the lump sum of \$500,000.
What's the decision? The lump sum amount would need to exceed \$573,496 to make it a better deal for the lot-
tery winner. The lump sum payout probably isn't negotiable, so (based on an interest rate assumption of 6%) the
20 annual payments is a better deal for the lottery winner.
The PV calculation is very sensitive to the interest rate assumption, which is often unknown. For example, if the
lottery winner assumed an interest rate of 8% in the calculation, the present value of the 20 payments would be
\$490,907. Under this scenario, the lump sum would be a better choice.
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