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

Investment and Portfolio Analysis With the increasing economic downturn in the economy, the need of investment has increased considerable. The potential investors generally foregoes their current leisure and earnings and investment their earnings and expect to earn benefits in future for the same. For analyzing the investment, we have taken into consideration a hypothetical investor who has $50,000 which needs to be invested in different, in different assets. Investment is one of the

Failing to contribute the maximum amount to this retirement plan is simply giving up on free money; by doubling his current contribution of three percent, Chris would actually be tripling the amount added to the 401(k) each year due to the employer's matching policy. This account is also earning an estimated eight percent annually, not far behind the 9.5% the stock market is expected to earn, and the money

Part Two At 35 years, all equities will be purged from the portfolio to maximize safety (10% corporates, 70% Treasuries, 20% cash). This means that the fund will generate an average return of (0.48+2.31+.1) = 2.89% Using Excel, it is determined that the value of the portfolio when John and Mary retire and Paul enters assisted living needs to be $5,775,134. With that level, the portfolio will have money until Paul turns

Investment Portfolio For this client, the total investment is $100,000. This is not the sum total of the investor's assets, but it will be invested in a diversified portfolio. It is assumed that the time horizon is medium-to-long-term. The investment portfolio will be built using the top-down approach, whereby asset classes are first determined and then the individual securities within those classes are determined subsequent. The first step in this process

9% for the past seven years (Index Mundi, 2009). An inflation rate of 2% per annum shall be assumed for our future cash flows model, the additional 0.1% reflecting a desire for conservativeness in our estimates. Karl's pension pays him 80% of his current salary, which is not expected to increase in the final three years. The pension benefit is indexed to inflation. We will assume a 30% tax rate for

By lowering interest rates, the government lowers the threshold of expected return for capital investments, thus making more investments economically viable. However, such supply side initiatives are weighed by firms against the potential income. If the economic outlook - that is to say the expected demand - is poor, such that the expected return will still not exceed the cost, then the investment will not be undertaken. In speaking with