Simple vs compound interest

Simple interest is calculated only on the original amount: principal × rate × time. 1,000 at 5% for 3 years earns 50 each year, so 150 in total, giving a final amount of 1,150.

It is common in short-term loans and some bonds, where interest is paid out rather than added to the balance.

With compound interest, earned interest is added to the balance and then earns interest itself. The balance after t years is P × (1 + r ÷ n)^(n × t), where n is how many times a year interest is added.

1,000 at 5% compounded yearly for 3 years grows to 1,157.63. That is 7.63 more than simple interest, and the gap widens every year.

Compounding is slow at first and fast later. 1,000 at 5% compounded monthly becomes about 1,647 after 10 years, but about 2,712 after 20 years — the second decade earns far more than the first.

This is why starting early matters so much for savings, and why debts with compounding interest can grow quickly when left unpaid.

More frequent compounding gives a little more growth. At 5% on 1,000 for one year you get 1,050.00 with yearly compounding, 1,051.16 with monthly and 1,051.27 with daily.

The difference between monthly and daily is small. The rate and the length of time have a much bigger effect than the compounding frequency.