Simple interest & compound interest

Bond Valuation and Analysis in Python

Joshua Mayhew

Options Trader

Simple interest

Simple interest depends only on the initial deposit or loan.

We deposit USD 1,000 in a savings account

The account pays 5% simple interest each month

How much interest will we have earned after 1 year?

How much will our account be worth?

$PV$ = Present Value = how much our money is worth today

$FV$ = Future Value = how much our money is worth in the future

$r$ = Interest Rate Per Period

$n$ = number of periods

$\text{Simple Interest Earned} = PV \times r \times n$

$\text{Future Value = Present Value + Simple Interest Earned}$

pv = 1000
r = 0.05
n = 12
interest = pv * r * n
print(interest)

fv = pv + interest
print(fv)

Compound interest means earning interest on our interest!

Deposit USD 1,000 in a bank account earning 5% compound interest per month.

Month	Starting Amount	Interest Earned	Ending Amount
1	1,000.00	1,000.00 * 0.05 = 50.00	1,000.00 + 50.00 = 1,050.00
2	1,050.00	1,050.00 * 0.05 = 52.50	1,050.00 + 52.50 = 1,102.50
3	1,102.50	1,102.50 * 0.05 = 55.13	1,102.50 + 55.13 = 1,157.63
...	...	...	...
12	1,710.34	1,710.34 * 0.05 = 85.52	1,710.35 + 85.52 = 1,795.86

USD 1,795.86 – USD 1,000.00 = USD 795.86 in compound interest

For 1 Period:

1,000 + (1,000 * 0.05) = 1,000 * 1.05 = 1,050

For 2 Periods:

1,050 * 1.05

= 1,000 * 1.05 * 1.05

= 1,000 * 1.05 ^ 2

For n Periods:

1,000 * 1.05 ^ n

The General Formula:

$FV = PV \times (1 + r)^n$

pv = 1000, r = 0.05, n = 12
fv = pv * (1 + r) ** n
print(fv)

1795.86

Bond Valuation and Analysis in Python