Microsoft Word - Money, Banking, and Int Finance(scribd).docx

Money, Banking, and International Finance

Of course, we could solve for the interest rate using the Rule of 72. For example, which
interest rate do you need for your savings account to double in 5 years? Your interest rate must
be 14.4% annually, or 72 ÷ 5.
We could apply the Rule of 72 to economic variables other than financial securities. For
example, the Chinese economy grows 10 % per year. How many years does Chinese economy
need to double in size? The Chinese economy doubles every 7.2 years, or 72 ÷ 10. On the other
hand, the U.S. economy grows slowly at 1% per year after the 2008 Financial Crisis. How many
years does the U.S. economy double in size? The U.S. economy doubles in size every 72 years,
or 72 ÷ 1. What would happen if the U.S. economy begins contracting in size by 1% per year?
We cannot use the Rule of 72 for negative growth rates. It is impossible for something to double
in size with a negative growth rate.

Multiple Investments

We can alter the analysis, so people receive or pay multiple future payments. For instance,
you deposit $500 into the bank account every year at 6% interest.

 After the first year, you earn $500 × 0.06 = $30 in interest. Your balance grows into $500 +

$30 + $500 = $1,030 because you have the initial $500, and then you deposited another

$500 at the end of the year into your account.

 After the second year, you earn $1,030 × 0.06 = $61.80 in interest. Your balance grows

into $1,030 + $61.80 + $500 = $1,591.80. You added another $500 to your account at the

end of the year.

 After the third year, you earn $1,591.80 × 0.06 = $95.508 in interest. Your balance

becomes $1,591.80 + $95.508 + $500 = $2,187.31. You added the last $500, which did not

earn interest.

We calculate the future value of your bank deposits in Equation 8.

ܸܨଷ=$500( 1 + 0. 06 )ଷ+$500( 1 + 0. 06 )ଶ+$500( 1 + 0. 06 )ଵ+$500( 1 + 0. 06 )଴ ( 8 )

ܸܨଷ=$2, 187. 31

Last term in Equation 8 is the final deposit. Although you multiply this term by an interest
rate, the exponent equals zero setting the term inside the parenthesis to a one. Consequently, the
exponent indicates how many years of interest that specific $500 earned over the course of three
years.
We can reverse our logic and calculate the value of these cash flows today if you receive
$500 now, $500 in one year, $500 in two years, and $500 in three years. We calculate the
present value of $1,836.51 in Equation 9.