Example 4

EXAMPLE 4 Compound Interest for Several Years

Suppose that you have a principal of $P = $ 1000$ invested at 10% nominal interest per year. Using the compound interest formula $A = P {(1 + i)}^{n}$ , we determine the amount in the account after 10 years, for annual, quarterly, and monthly compounding.

Annual compounding. The annual rate of 10% gives $i = 0.10$ , and after 10 years, the account has

$$ 1000 {(1 + 0.10)}^{10} = $ 1000 {(1.10)}^{10} \approx $ 2593.74$
Quarterly compounding. Then $i = r / m = 0.10 / 4 = 0.025$ , and after 10 years ( $m t = 4 \times 10 = 40 quarters$ ) the account contains

$$ 1000 {(1 + \frac{0.10}{4})}^{4 \times 10} = $ 1000 {(1.025)}^{40} \approx $ 2685.06$
Monthly compounding. Then $i = r / m = 0.10 / 12 \approx 0.008333$ . The amount in the account after 10 years ( $m t = 12 \times 10 = 120 months$ ) is

$$ 1000 {(1 + \frac{0.10}{12})}^{12 \times 10} \approx $ 2707.04$

These entries are found in the last row of Table 21.2 on page 873.