Final answer:
The greatest gain on money in a savings account occurs when interest is compounded daily. Daily compounding allows interest to be added to the account balance more often, resulting in more interest earned over time. More frequent compounding leads to greater investment growth than less frequent compounding intervals.
Step-by-step explanation:
The greatest gain on money in a savings account occurs when interest is compounded daily. This is because compounding more frequently means that interest is being calculated and added to the account balance more often, which leads to an increased amount of interest earned over time.
When interest compounds daily, each day's interest can earn interest on the following day, which accelerates the growth of the investment compared to compounding quarterly, semi-annually, or annually.
For example, if you start with an initial investment of $3,000 and assume a 7% real annual rate of return, compounded annually, after 40 years, you would have:
3,000(1+.07)
40
= $44,923
The more frequently the interest is compounded, the greater the total amount will be after the same period. Savings accounts with compound interest provide the benefit of earning interest on the interest, which is why it's advantageous to have an account where interest is compounded as often as possible.
Therefore the correct answer is 1) daily.