Compound Interest

Study guide: Exam FM-2

Under compound interest, interest earned in each period is added to the principal and itself earns interest in subsequent periods. An investment of $P$ at effective annual rate $i$ grows to:

$A(t) = P(1+i)^t$

The Accumulation Function is $a(t) = (1+i)^t$ , which is exponential (vs. linear under Simple Interest).
Compound interest is the standard convention for actuarial and financial calculations.
For $n$ periods at rate $i$ , $(1+i)^n$ is the accumulation factor — the value at time $n$ of 1 invested now — and $v^n = (1+i)^{-n}$ is the present value of 1 due in $n$ periods, where $v = (1+i)^{-1}$ is the discount factor.

Comparing Simple vs. Compound Interest $1{,}000$ is invested for 3 years at 6% per year. Compare simple vs. compound accumulation.

Answer Simple: $1000(1 + 0.06 \times 3) = 1000(1.18) = 1180$

Compound: $1000(1.06)^3 = 1000(1.19102) = 1191.02$

Compound interest yields more because earned interest is reinvested.