What effect does compound interest more frequently than annually have on its future value and the effective annual rate (EAR)? Explain. How would you explain the difference between the annual percentage rate (APR) and effective annual rate (EAR) to a friend with no background in finance?

Compound interest allows interest to compound on itself over a specific holding period. As a result, owners of a particular asset earn interest on their original investment plus the interest that was accrued in prior periods. This creates a compounding effect that can take small sums of money and overtime, create very large sums of money (Belser, 1919). For example, a $1000 investment that earns 5% per year will earn $1050 at the end of one year. However, at the end of the second year the investment will be $1102.50. The interest in year two was 5% more than interest in year one, which is then added to the original equity investment of $1000. Essentially, interest is earning interest. The longer and more frequently this occurs the large the sums of money at the end of the holding period. Due to this concept, the earlier an individual starts investing, the more opportunity they have for compounding to take effect for them over the long term. The frequency of the compounding has a beneficial effect on the future value and effective annual interest rate. By compounding more frequently, the interest and principle amounts have more opportunities to earn interest on interest. For example, a 6% bond that compounds quarterly will have four opportunities to earn interest as compared to the same bond that only compounds annually. This creates variations in the effective annual rate which accounts for the periodic compounding through the year as compared to the annual percentage rates which is simply the annual rate of return. Essentially the effective annual rate takes into account compounding while the APR in an annual percentage rate that does without accounting for the periodic compounding periods.

References

1. Belser, F. C. 1919. Rapid calculation of compound interest processes.Journal of Accountancy(April): 241-248