NOMINAL

Returns a nominal interest rate given the effective compounded interest rate.

Syntax:

NOMINAL(eff_rate, num)

eff_rate: the effective interest rate.

num: the number of times interest is credited / compounded during the period that the nominal rate applies to.

If an investment has a nominal rate, say for a year, but interest is paid and credited say each quarter, the interest paid each quarter will itself start earning interest. This increases the effective value. The effective rate is the rate that would have to be paid at the end of the (say) year to give the same return.

Given an effective rate, this function returns the appropriate nominal rate.

The formula used is:

$n o m_r a t e = n u m [(1 + e ff_r a t e)^{1/ n u m} - 1]$

Example:

NOMINAL(6%; 4)

returns approximately 5.87%, which is the nominal rate for an investment with a effective rate of 6% per annum, compounded quarterly.

Application:

Comparing Loan Offers

Imagine you are looking for a personal loan and have received two different offers. To make an apples-to-apples comparison, you need to understand their nominal interest rates.

Scenario:

Bank A offers a loan with an effective annual interest rate of 7.5%, compounded monthly.
Bank B offers a loan with a nominal annual interest rate of 7.2%, compounded quarterly.

You want to find the nominal rate for Bank A's offer to compare it directly with Bank B's.

Using the NOMINAL Function:

We will use the NOMINAL function to find the nominal interest rate for Bank A.

Effective Rate: 7.5% or 0.075
Compounding Periods: 12 (monthly)

The formula we would use in a spreadsheet is: NOMINAL(0.075, 12)

Calculation:

$Nominal Rate = 12 \times [(1 + 0.075)^{(\frac{1}{12})} - 1]$

$Nominal Rate \approx 12 \times [(1.07 5^{0.08333}) - 1]$

$Nominal Rate \approx 12 \times [1.006045 - 1]$

$Nominal Rate \approx 12 \times 0.006045$

$Nominal Rate \approx 0.07254 or 7.254%$

Analysis Table

Here's how you could set up a table to compare the two loan offers side-by-side:

	Feature	Bank A	Bank B
	A	B	C
1	Effective Annual Rate (EAR)	7.50%	7.20%
2	Compounding Periods	Monthly (12)	Quarterly (4)
3	NOMINAL Function	NOMINAL(7.5%, 12)	NOMINAL(7.20%, 4)
4	Calculated Nominal Rate	7.254%	7.013%
5	Conclusion	Higher Nominal Rate, but also higher EAR.	Lower Nominal Rate, but also lower EAR.

Conclusion from the Example

Even though Bank A has a higher nominal interest rate (7.254%) compared to Bank B (7.013%), its effective interest rate is significantly higher due to the more frequent compounding.

This example shows that you can't compare two loans with different compounding frequencies using just the nominal rate. To accurately compare them, you can either use the NOMINAL function to convert a loan with an effective rate to a nominal rate, or use the EFFECT function to convert a loan with a nominal rate to an effective rate.