A Small Detour: Savings Account and Interest Compounding
A typical way to think about interest rates is to study how a savings account works. Suppose Mr. X puts $1000 in a savings account that provides a one percent annual interest rate. In that case, X will get at the end of:
- Year 1: $1010 = $1000(1 + 0.01)
- Year 2: $1020.1 = $1010(1 + 0.01) = $1000(1.01)2
- Year 5: $1051.01 = $1000(1.01)5
Several things are worth noticing:
- The rate of return is fixed by the issuer of the account (1%)
- Principal rises over time: The longer X keeps the funds in his saving account, the greater, the total amount of principal due by a bank when X chooses to withdraw all its funds.
- Income rises over time: Interest income earned is automatically added to the outstanding amount of funds ($1000, $1010, etc.) so income earned changes every year as more funds are accumulated: $10 the first year, $10.1 the second year, $10.2 the third year…
Most securities work quite differently.