# Calculate Compound Interest in Python (3 Examples)

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: Final Amount
• P: Initial Principal
• r: Annual Interest Rate
• n: Number of compounding periods per year
• t: 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.