Question

Eckelberger Products Inc. makes high speed recorders with high-speed scanning. The small company has been growing at an average rate of 65% per year for the past 4 years. The CEO asked you to convert the past growth rate into a quarterly rate for its annual report. If the past growth rate was an effective rate, what was the effective growth rate quarterly? The effective growth rate quarterly is %.

Answer 1

BACKGROUND: The Effective Annual Growth Rate, or EAR, for the company for previous 4 years is 65%. We need to find the effective growth rate for the quarter.

FORMULA:

I - ul; +1) = ?

where, n = Number of periods, and r = rate

SOLUTION TO THIS QUESTION:

n = 4 (Since number of Quarters in a year = 4, hence, compounded 4 times)

Annual Rate = 0.65 [Value is in decimal form and not percent form (65% / 100)]

Hence, the answer is:

0.65. i = (1+

i = 82.6299%

(Please note that the answer mentioned has been derived assuming that you need Effective Annual Rate Compounded Quarterly. Since there is no mention of the words "annual" and "compounded", I presume you do not need the quarterly interest rate but EAR compounded quarterly.)

EXTRA KNOWLEDGE: Effective Annual Rate (EAR) is also known as Effective Annual Interest Rate or the Annual Equivalent Rate (AER). For continuous compounding, use the formula

i=e" - 1

Thank you.