Abstract The article says that it is good educational psychology to explain difficult topics by simple diagrams. Diagrams in economics books have long explained the forces of supply and demand. Diagrams have frequently showed the circulation of money. There is, in fact, no value in keeping a thing difficult that might he made simple and easily understood by a diagram. The article further says that annuities constitute the axis of the entire field of actuarial science. Innumerable business problems are entirely or in part annuities and they are found in accounting and insurance, and even in corporation finance and public finance. The article presents a diagram to reveal their exact nature and which can be remembered much longer than any well-worded page. The graphic method of showing annuities can be used for many types of annuities and kinds of problems. The horizontal scale gives the time in periods from left to right. The vertical scale is used only to show the sequence of rents of the annuity, the first at the top and the last at the bottom. The interest is shown as an addition to the rents in order to give the final amount or as an addition to the initial present worth in order to give the rents.

Abstract The article focuses on interpreting the two principal annuity formulas. It is assumed that the student already understands the formulas for compound interest and compound discount and recognizes them in the said formulas. For calculating annuity, most of the students employ the formula for the sum of a geometric progression. However, the two principal annuity formulas can be explained without reference to a geometric progression and in terms that a student can understand and remember. Without referring to a geometric progression, the author attempts to show why the first formula is compound interest on one divided by the interest rate per period and why the second formula is compound discount on one divided by the interest rate per period. The author believes that the explanations presented in the article are preferable to the usual textbook discussion because the student can see why the annuity formulas are as they are; namely, compound interest on one divided by the interest rate per period and compound discount on one divided by the interest rate per period.