“Compound interest is the eighth wonder of the world. He who understands it, earns it … he who doesn’t … pays it.” – Albert Einstein

#### Key Terms

**Compound Interest**: Interest calculated on the initial principal and on the accumulated interest from previous periods.

**Principal**: The original amount invested or borrowed, separate from earnings or interest.

**Time-Value of Money**: A core financial tenet inferring money available in the present is worth more than an equal amount in the future because of potential earnings over time. Essentially this means putting a $10,000 away today is worth more than putting away $10,000 in five years.

#### The Time-Value of Compound Interest

First we’ll examine simple interest or a scenario in which * only the principal earns interest.* Let’s say a bank exists offering 10% interest. For simplicity, let’s also imagine we invest $1,000 over 5 years.

Principal | Interest on Principal | Past Interest Earning Interest | Total Annual Return | |
---|---|---|---|---|

Year 1 | $1000 | 1000 * (.10) = $100 | $0 | 1000 + 100 = $1100 |

Year 2 | $1000 | 1000 * (.10) = $100 | $0 | 1100 + 100 = $1,200 |

Year 3 | $1000 | 1000 * (.10) = $100 | $0 | 1200 + 100 = $1,300 |

Year 4 | $1000 | 1000 * (.10) = $100 | $0 | 1300 + 100 = $1,400 |

Year 5 | $1000 | 1000 * (.10) = $100 | $0 | 1400 + 100 = $1,500 |

The beauty of compound interest is that * past interest earns interest. *In the same hypothetical the interest will compound annually.

Principal | Interest on Principal | Past Interest Earning Interest | Total Annual Return | |
---|---|---|---|---|

Year 1 | $1000 | 1000 * (.10) = $100 | $0 | 1000 + 100 = $1,100 |

Year 2 | $1000 | 1000 * (.10) = $100 | $100 * (.10) = $10 | 1100 + 110 = $1,210 |

Year 3 | $1000 | 1000 * (.10) = $100 | $210 * (.10) = $21 | 1210 + 121 = $1,331 |

Year 4 | $1000 | 1000 * (.10) = $100 | $331 * (.10) = $33 | 1331 + 133 = $1,464 |

Year 5 | $1000 | 1000 * (.10) = $100 | $463 * (.10) = $46 | 1464 + 146 = $1,610 |

While this example is of a relatively small scale, by the end of the five years compounding interest earns an extra $110 (from 1610-1500 = 110). Simple interest allows linear growth, while compound interest allows exponential growth. An example of linear growth in finance would be the coupons paid on bonds. An example of exponential growth would be reinvesting stock dividends.

If we were to scale this example upwards in terms of time and initial principal the difference would become quite pronounced. A $10,000 principal invested over 40 years and earning 7% annually would result in $38,000 in simple interest…But if the interest were compounding, $149,744 would have been earned.

A classic example of the time value of money is Benjamin Franklin bequeathing a thousand sterling to his favorite two cities, Boston and Philadelphia in 1790. A thousand sterlings was the equivalent of about $4,400 at the time. Wanting to be useful even after death, he designed a trust allowing funds to be withdrawn from the accounts for housing and aspiring businessmen. Loans from the fund had to be paid with 5% interest. By 1990 Philadelphia’s trust was worth $2 million and Boston’s was worth $5 million.

#### Conclusions

Compounding interest may be considered the 8th Wonder of the World because it creates exponential growth. Understanding the time value of money and reinvesting earnings over time is one of the core principals of wealth creation. Simply when properly managed, **wealth earns wealth**. Benjamin Franklin’s trusts exemplify this mantra. I personally plan on using a Roth IRA as a tax free vehicle for compounding interest over my lifetime.

Investor.gov offers a compound interest calculator I often use as a resource.