Simple Interest

Study guide: Exam FM-2

Under simple interest, interest is earned only on the original principal — it does not itself earn interest. An investment of $P$ at rate $i$ per period grows to:

$A(t) = P(1 + it)$

Simple interest is linear in time, in contrast to Compound Interest which is exponential.
It is mainly useful over short periods, such as a fraction of a year, where it approximates compound interest: $(1+i)^t \approx 1 + it$ for $0 < t < 1$ . (Treasury bills are not an example — their yields are computed on a simple discount basis.)
The Accumulation Function under simple interest is $a(t) = 1 + it$ . When a question specifies simple interest, SOA measures $t$ from the moment each cash flow occurs, so a deposit $C$ made at time $s$ is worth $C\,[1 + i(t - s)]$ at time $t$ (see Accumulated Value).

Simple Interest Growth $2{,}000$ is invested at 8% per year simple interest for 9 months. Find the accumulated amount.

Answer $t = 9/12 = 0.75$ years: $A(0.75) = 2000(1 + 0.08 \times 0.75) = 2000(1.06) = 2120$