~RATE to YIELD MODEL

Description: There is a difference between the rate that is quoted on a financial instrument and the percent return, or effective yield, that the investor actually realizes from that same instrument. The difference is due to the effects of compounding interest, and the effective yield will be slightly greater than the quoted rate as long as the period between compounding is less than a year. This model is applicable to fixed rate instruments such as Certificates of Deposits (CDs).

The Model: Effective (annual ) yields may be derived from quoted (annual) rates and the frequency of compounding. The actual contractual holding period of the instrument is irrelevant because both the quoted rates and the effective yields are expressed on an annualized basis.

The model, (1+k)ⁿ-1 is derived from combining D /orig and FV=PV(1+k)ⁿ, where:

D = the difference between the original (beginning) value (PV), and the ending value (FV), after having been held for one year.

orig = the original beginning value (PV)

k = the rate for the period of compounding

n = the number of compounding periods

Note that the beginning value (PV) is also irrelevant, as it doesn't appear in the final model (it gets canceled out through algebraic reduction). Also, intuitively, the returns, or yields, on an instrument are not affected by multiples of the instrument.

Example: Calculate the effective yield on a three month CD, $5,000 denomination, with a quoted rate of 2.5%, compounded weekly.

(1+k)ⁿ-1

(1+.025/52)⁵²-1

(1.0004808)⁵²-1

1.0253089-1

.0253089

=2.53089 %

file: a:fin\rate2yld.doc eh26feb99