EFFECT

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

Syntax:

EFFECT(nom_rate, num)

nom_rate: the nominal interest rate.

num: the number of times interest is credited / compounded during the period that nom_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. This function returns the effective rate - that is, the rate that would have to be paid at the end of the (say) year to give the same return.

The formula used is:

$e ff ec t i v e_r a t e = (1 + n o m_r a t e / n u m)^{n u m} - 1$

Example:

EFFECT(6%, 4)

returns approximately 6.14%, which is the effective rate of an investment with a nominal rate of 6% per annum, compounded quarterly.

Application:

Comparing Loan Options

Imagine you are looking for a personal loan and have received two offers from different banks. You want to determine which loan has the lower effective annual interest rate.

Loan Option A:

Nominal Interest Rate: 8.00%
Compounding Frequency: Monthly (12 times per year)

Loan Option B:

Nominal Interest Rate: 8.10%
Compounding Frequency: Quarterly (4 times per year)

You can use the EFFECT function to calculate the effective annual rate for each loan. The EFFECT function uses the following syntax:

EFFECT(nominal_rate, npery)

nominal_rate is the stated annual interest rate.
npery is the number of compounding periods per year.

Calculation

For Loan Option A:

EFFECT(8.00%, 12)
This calculates the effective rate for an 8.00% nominal rate compounded monthly.

For Loan Option B:

EFFECT(8.10%, 4)
This calculates the effective rate for an 8.10% nominal rate compounded quarterly.

Results Table

	Loan Option	Nominal Rate	Compounding Frequency (npery)	EFFECT Formula	Effective Annual Rate (EAR)
	A	B	C	D	E
1	A	8.00%	Monthly (12)	EFFECT(0.08, 12)	8.3%
2	B	8.10%	Quarterly (4)	EFFECT(0.081, 4)	8.349%

Conclusion

Although Loan Option B has a higher nominal rate (8.10% vs. 8.00%), its lower compounding frequency results in a slightly higher effective annual rate. The effective rate for Loan A is 8.3%, while the effective rate for Loan B is 8.349%.

Therefore, Loan Option A is the better choice as it has a lower effective interest rate, meaning you will pay less in interest over the course of the year. The EFFECT function is crucial for making an accurate, apples-to-apples comparison of financial products with different compounding periods.