Say that the annual rate is \(5 \%\), and we invest \(\$ 1000\) for two years. The wealth at the end of the holding period depends on how the interest rate is applied. Under the simple interest rate rule of Eq. (3.1), wealth after two years is

If interest is paid annually and it may be immediately reinvested, wealth after two years will stem from the application of Eq. (3.2), 

The slight difference between the two amounts is due to the compounding mechanism, since 

and the term \(r^{2}\) corresponds to interest earned on interest.

Data From Equation (3.1)

Data From Equation (3.2)

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==== L (1+2r) = 1000 (1+2 x 0.05) = $1100.