# Python Compound Interest

Compute compound interest using a formula. Compound on different time schedules.**Compound interest.** There is a time value of money. This is interest. In compound interest, an investor earns interest on top of the interest already earned.

**A formula.** The compound interest formula is well-known—it is an exponential function. In Python the pow method is needed. We translate this formula into a Python def.

Numbers: pow**Our program.** The compound_interest method computes the total value of the money (principal) after interest is paid. We specify the rate (the interest rate, expressed as a percentage).

**Rate:** This is the interest rate. For an interest rate of 4.3%, we can pass 0.043.

**Times:** The times_per_year argument indicates yearly (1), quarterly (4) or monthly (12) interest.

**Years:** This final argument to compound_interest tells us how many years we compound interest. Thinking long-term is important.

**Python program that computes compound interest**
def __compound_interest__(principal, rate, times_per_year, years):*
# (1 + r/n)
*body = 1 + (rate / times_per_year)*
# nt
*exponent = times_per_year * years*
# P(1 + r/n)^nt
*return principal * pow(body, exponent)*
# Compute 0.43% quarterly compound interest for 6 years.
*result = compound_interest(1500, 0.043, 4, 6)*
# Write result.
*print(result)
print()*
# Compute 20% compound interest yearly, quarterly and monthly.
*print(compound_interest(1000, 0.2, 1, 10))
print(compound_interest(1000, 0.2, 4, 10))
print(compound_interest(1000, 0.2, 12, 10))
**Output**
1938.8368221341054
6191.7364223999975
7039.988712124658
7268.254992160187

**Verification.** I could write all sorts of incorrect code on this website, but this would not do anyone any good. The result to the first call (above) matches Wikipedia's example.

Compound interest: Wikipedia**Yearly, quarterly, monthly.** In the last three calls to compound_interest above, we compare how the final amount of money changes based on how often interest is paid.

**And:** Monthly and quarterly interest accumulates much faster than yearly interest. So this metric is important in an investment.

**Tip:** This comparison can help us judge certain investments. For example, bonds may pay monthly, but dividend stocks quarterly.

**In volatile markets,** an investment's interest rate may appear irrelevant. And this is often true. Capital appreciation too is important.

**Compounding.** The concept of compound interest is behind much of the world's capital markets. It motivates investment. Compound interest is a powerful generator of wealth.

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