Balance = B0(1 + i)t
where B0 is the beginning balance in the account, i is the periodic interest rate, and t is the number of periods that have passed.
If the begining balance in the account is $125, and the account earns 3% interest per year, compounded daily, what will be the balance after 1 year? After 50 years? When does the balance reach $500?
Balance after 50 years = 125(1 + .03/365)18250 = $560.18
Balance reaches $500 when t = −ln(4)/(ln(36500/36503)) = 16867.27 days, or about 46.2 years
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