*23*

We can use the following compound interest formula to find the ending value of some investment after a certain amount of time:

**A = P(1 + r/n) ^{nt}**

where:

**A:**Â Final Amount**P:**Â Initial Principal**r:**Â Annual Interest Rate**n:**Â Number of compounding periods per year**t:**Â Number of years

We can use the following formula to calculate the ending value of some investment in Python:

P*(pow((1+r/n), n*t))

And we can use the following function to display the ending value of some investment at the end of each period:

def each_year(P, r, n, t): for period in range(t): amount = P*(pow((1+r/n), n*(period+1))) print('Period:', period+1, amount) return amount

The following examples show how to use these formulas in Python to calculate the ending value of investments in different scenarios.

**Example 1: Compound Interest Formula with Annual Compounding**

Suppose we invest $5,000 into an investment that compounds at 6% annually.

The following code shows how to calculate the ending value of this investment after 10 years:

#define principal, interest rate, compounding periods per year, and total years P = 5000 r = .06 n = 1 t = 10 #calculate final amount P*(pow((1+r/n), n*t)) 8954.238482714272

This investment will be worth **$8,954.24** after 10 years.

We can use the function we defined earlier to display the ending investment after each year during the 10-year period:

#display ending investment after each year during 10-year period each_year(P, r, n, t) Period: 1 5300.0 Period: 2 5618.000000000001 Period: 3 5955.08 Period: 4 6312.384800000002 Period: 5 6691.127888000002 Period: 6 7092.595561280002 Period: 7 7518.151294956803 Period: 8 7969.240372654212 Period: 9 8447.394795013464 Period: 10 8954.238482714272

This tells us:

- The ending value after year 1 was
**$5,300**. - The ending value after year 2 was
**$5,618**. - The ending value after year 3 was
**$5,955.08**.

And so on.

**Example 2: Compound Interest Formula with Monthly Compounding**

Suppose we invest $1,000 into an investment that compounds at 6% annually and is compounded on a monthly basis (12 times per year).

The following code shows how to calculate the ending value of this investment after 5 years:

#define principal, interest rate, compounding periods per year, and total years P = 1000 r = .06 n = 12 t = 5 #calculate final amount P*(pow((1+r/n), n*t)) 1348.8501525493075

This investment will be worth **$1,348.85 **after 5 years.

**Example 3: Compound Interest Formula with Daily Compounding**

Suppose we invest $5,000 into an investment that compounds at 8% annually and is compounded on a daily basis (365 times per year).

The following code shows how to calculate the ending value of this investment after 15 years:

#define principal, interest rate, compounding periods per year, and total years P = 5000 r = .08 n = 365 t = 15 #calculate final amount P*(pow((1+r/n), n*t)) 16598.40198554521

This investment will be worth **$16,598.40 **after 15 years.

**Additional Resources**

The following tutorials explain how to perform other common tasks in Python:

How to Calculate Z-Scores in Python

How to Calculate Correlation in Python

How to Calculate a Trimmed Mean in Python