Keynes marveled at the way compound interest facilitated the accumulation of capital which made the modern era possible  [see Keynes, “Economic Possibilities for our Grandchildren“ ] What he was really talking about is the growth that is possible when profits from an enterprise are re-invested rather than spent on consumption. [see Growth] Adding unpaid interest to the loan balance in order to calculate a new amount of interest due is not quite the same as re-investing profits. Conceptually it is like constantly refinancing a loan. It is the flip side of what happens when interest credited to a savings account is left in the account and included in the balance used to calculate the next interest payment.

Perhaps the most common application of compound interest other than a savings account is in the calculation of mortgage payments where part of each payment pays down the principal on the loan so the amount of interest due at the next payment is less. This is a simply payment plan which enables the borrower to pay off the whole loan with fixed periodic payments. Recalculating the loan with each payment in this case seems to benefit the borrower since the total amount of interest paid is less than it would be with an interest-only loan with a balloon payment of principal at the end of the term.

Compound interest is used with certain types of bonds like zero coupon bonds where the interest is recalculated periodically and paid out at the end of the term. It may also be used in calculating the interest on credit card debt where it may be compounded daily.

Compound interest on loans and bonds only exists because financial markets allow them to. There is no more inherent logic to compound interest than there is to interest of any other sort.

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