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# Lesson 4-Compound Interest and Fees

Updated: Oct 15, 2021

Compounding interest example
.xlsx

Compound interest is the interest an investor earns on their original investment and on the interest earned in previous periods. In contrast to simple interest, which is interest earned on the principal only, compound interest is earned on the principal and on interest accumulated in previous periods. Simply, money made in previous periods makes money, accelerating the growth of an investment over time. This concept is difficult to understand so an example has been provided below.

Simple interest is interest earned on the original principal only. For example, if an individual deposits \$150,000 into a high-interest savings account at a 10.504% simple interest rate for 14 years, the interest earned each year is \$15,756 which is 10.504% of \$150,000 (refer to excel file).

If an investor deposits \$150,000 into a portfolio yielding 10.504% interest compounded annually. In year 1, the interest earned would be \$15,756. However, in year 2, the interest earned would be 10.504% of \$165,756, which includes the original \$150,000 and the \$15,756 interest earned in year 1, resulting in \$17,411 earned in interest in year 2. In year 3, interest is earned on the principal and on the interest earned in years 1 and 2, resulting in interest earned in year 3 increasing to \$19,239.87. This trend continues with interest earned in each period growing at an exponential rate or increasing at an increasing rate, (i.e. 2,4,8,16, the difference between each number in this sequence is growing at an exponential rate). By the 14th year, interest earned increases to \$57,724.47 as interest is earned on the principal and on all the interest earned in previous years.

Online calculators can be used to demonstrate the long-term effects of compound interest. As seen in figure 1, a principal investment of \$150,000 and monthly contributions of \$500 in a portfolio yielding 10.504% compounded annually will grow to \$1,469,686.50 by year 20, with monthly contributions totaling \$170,000. Increasing levels of interest are earned each year (refer to figure 2), resulting in the principal growing to \$4,088,258.46 by year 30. This demonstrates how investors with longer time horizons will benefit more from compound interest as larger amounts in interest are earned in later years. By year 50, \$2,904,698.04 is earned in interest, resulting in the principal growing to \$30,500,833.22, with monthly contributions totalling \$450,000 (refer to figure 3). In general, investors will only realize significant gains from compound interest after 10-15 years, the longer an investor's time horizon the more they will earn in interest.

Effect on Fees (refer to excel file):

Expense ratios are the annual fees an investor pays to the issuing company (i.e. Vanguard or Blackrock) for investing in their ETF. They are charged as a percentage of the investment, for example, an ETF with a 0.15% expense ratio will charge 0.15% annually on the invested amount. Fees on an investment compound annually, therefore portfolios with lower expense ratios incur significantly lower fees. Using the portfolio from the previous example and applying a 0.15% expense ratio results in total fees over 14 years coming to just \$7,215.877, or 1.578% of all capital gains. In contrast, total fees incurred from a higher expense ratio of 1% over the 14 years come to \$48,105.85 or 10.52% of all capital gains. Over longer periods, fees further increase and reduce profits. This demonstrates how small differences in fees can significantly reduce profits. As a result, portfolios should be designed to maximize returns while minimizing fees. Outlined in article 5 is a portfolio designed for young investors, with a forecasted long-term return of 16.48% and an expense ratio of 0.15%. Figure 1 - Compounding Returns in First 20 Years Figure 2 - Compounding Returns in Following 10 Years Figure 3 - Compounding Returns by 50th Year