Calculating Nominal and Effective Forward Interest Rates

Summary

The document asks how to derive a forward rate for a future interval from quoted money-market rates across several maturities. It gives rates for three, six, nine, and twelve months, then sets up a compounding equation to infer the nominal rate applying from month three through month nine. This illustrates the basic no-arbitrage relationship: investing over the full horizon should match investing over the initial period and then reinvesting at the implied forward rate.

The question also distinguishes a nominal annualized quote from an effective rate over the forward interval. These are not automatically identical: conversion depends on the compounding convention and the length of the accrual period. The document contains no answer or worked numerical result, and the quoted-rate conventions are not fully specified, so a unique effective rate cannot be confirmed from the prompt alone.

Key ideas

• A forward rate can be inferred by equating accumulation over a full term with accumulation over consecutive subperiods.
• The implied forward rate depends on the compounding basis used for the market quotes.
• A nominal annualized rate and an effective rate over a period are distinct unless their conventions make them coincide.
• The rate quotes alone do not resolve the calculation unless their day-count and compounding conventions are known.

Tags

# Hot do I calculate an effective forward rate?


# Hot do I calculate an effective forward rate?












I have to find nominal and effective forward interest rate for 3M-9M term, knowing that current interest rates are:

- 3M - 2.05%

- 6M - 2.04%

- 9M - 2.03%

- 12M - 2.02%

For a nominal interest rate I just solve for $r$ the following equation:

$$(1+\frac{2.05\%}{4})(1+\frac{r}{2})=(1+2.03\%\cdot\frac{3}{4})$$

I will have some $r$ (nominal i.r.) but how can I find an effective interest rate? Won't it be the same as nominal?

Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)

This summary was written by Stratmill's research agent from the original; it is not a copy of the source.