4 Money and Numbers: Primer

A basic understanding of economic cycles, business cycles, and financial instruments is central to the cognizant, hands-on approach to money that is often encountered by arts professionals. Interest rates (specifically, annually compounded interest rates) will be used to quantify characteristics unique to specific investment vehicles and economic indexes.

Interest rates can be presented in different ways, for convenience or as a convention of a certain sector.  In the mathematics involving interest rates, for example, finance professionals and actuarial scientists use different variable names to describe the same idea of a compound interest rate.  A theoretical inflation rate of 2% represents 2 parts from 100 (or 0.02), and the corresponding output of applied inflation could be presented with equal precision as 1.02 or 102%.  Though the distinction is arbitrary and intended for clarity, rates will be presented generally using decimal form when used in computation.

Where a percent reflects a proportion between a number and 100, a percent change denotes not just the difference between new and old percent, but the ratio between them.  If an interest rate changes from 10% to 15%, the percent change is not 5%; rather:

[latex](0.05 ÷ 0.1)= 0.5[/latex], and [latex](0.5 × 100)=50[/latex]%, which more adequately depicts the relative change in interest rates.  A basis point, another term often encountered when reviewing prospectuses for financial instruments, represents one hundredth of a percent: 0.01%, or 0.0001 in decimal form.

In exchange for temporary control of money, interest is paid to the owner of the asset periodically as a percentage of the asset.  Simple interest means that the interest rate is calculated only on the principal, or initial investment.  In compound interest, however, interest is paid as a percentage of an asset’s current value, including any interest previously accrued.

Compound interest is perhaps the most valuable tool at the investor’s disposal, especially when coupled with time.

In example, consider an account with a principal investment of $1,000.00.  When earning a simple annual (yearly) interest rate of 10%, that account will have a value of $1,100.00 at the end of the first year, $1,200.00 at the end of the second year, and $1,700.00 at the end of the seventh year.

If instead applying compound interest, however, an account starting with the same $1,000.00 and an annual compounding interest rate of 10% would have $1,100.00 at the end of the first year; but, the second year would earn interest both on the initial principal ($1,000.00) and the interest ($100.00), meaning the account would have a value of $1,210.00 at the end of year two and roughly $2,000.00 at the end of seven years.

When considering compound interest, the rule of seventy-two describes the relationship between interest rate and time, wherein an investment with a 10% annual return will double in value at roughly 7.2 years; and, an investment with a 7.2% annual return will double in value after roughly 10 years.  This shorthand method of computation can prove useful in estimating the future value of an investment when the interest rate is close to 7.2% or 10%, or when estimating the interest rate after determining that an investment needs to double in a certain amount of time.

As presented in the above rule, any variable in a mathematical equation may be the subject of inquiry based on the needs of the investor.  If an investor is on the hunt for a particular interest rate, they should also be wary of their intended time horizon, or how long an investment will stay active before the asset is needed elsewhere.

An initial investment of $1,000.00, held at an annually compounded interest rate of 7.2%, would double in value to $2,000.00 at roughly ten years; this means that the new account value would be only half made up of the principal investment—half of the new value comes from accrued interest.  After another ten years (twenty years from the initial investment), the new value would be roughly $4,000.00—consisting of a $1,000.00 principal investment and $3,000.00 of accrued interest.  As the time horizon of an investment expands (longer time periods are considered), the chasm grows, and an investment’s value is made up almost entirely of interest.