Simple vs. Compound Interest: Fundamentals for Actuaries
Compare simple and compound interest and their formulas for Exam FM.
Simple Interest
Under simple interest, the accumulation function is a(t) = 1 + it, where i is the interest rate and t is time. Interest is earned only on the original principal, not on accumulated interest. For example, $1000 at 5% simple interest for 3 years accumulates to 1000(1 + 0.05*3) = $1150.
Simple interest is rarely used in practice for periods longer than one year, but it commonly applies for fractional periods, such as exact interest calculations for days within a year. The effective rate per period under simple interest is not constant, which is why compound interest is preferred for multi-period problems.
Compound Interest
Under compound interest, a(t) = (1 + i)^t. Interest earned in one period itself earns interest in subsequent periods. For $1000 at 5% compound interest for 3 years: 1000(1.05)^3 = $1157.63. The extra $7.63 compared to simple interest is "interest on interest."
Compound interest is the standard on Exam FM. Unless stated otherwise, assume compound interest. The effective interest rate in each period is constant at i, which is a defining property of compound interest.
Comparison and Exam FM Tips
For t < 1, simple interest produces a larger accumulation than compound interest (1 + it > (1+i)^t). For t = 1, they are equal. For t > 1, compound interest gives more. This crossover is occasionally tested on Exam FM. In problems involving both simple and compound interest, identify which applies to each segment of time. A common setup: compound interest for whole years and simple interest for fractional years.