Question

For problem in the book Foundations of Financial Management, 16th ed., Chapter 9, problem 25P, how is the compounding period of 40 calculated and also the interest rate 0.03 (in the solution). The problem reads calculate the future value of $20,000 with 12% yearly return after 10 years, if the interest is compounded quarterly. Thanks.

Answer 1

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Hi, Since you want to understand the compounding of rates , first understand what is compounding and how it works.

Compounding meaning: Compounding is a financial terms usually used in the calculation of interest under which interest is provided for a given period and after that period total sums i.e. Principal and interest becomes the principal for the next compounded period. Lets take an example, if compounded is annually, a sum of $100 is invested at Rate of 5%, so interest is calculated for a year and after 1 year it becomes $105 and for the second year interest will be calculated on $105 at 5% rate.

In the same fashion, if compounded is semiannual then there is 2 semiannual period in a year so Year is multiplied by 2 and rate is divided by 2, so we will calculate interest on $100 for 1 semiannual period at rate of 5%/2 = 2.5%, which becomes 102.5 at first semiannual period and again interest for 2 semiannual period will be calculated on $102.5 at rate of 2.5% which becomes $105.0625 in that way it is more than $105 that is calculated if compounding is annual. If compounded period is further increased at quarterly compounding, now there is 4 quarter in a year and interest is provided for each quarter and rate is divided by 4 i.e. on $100 for 1 quarter rate will be calculated on 5%/4 = 1.25% that is 100 x 1.0125 = $101.25 for the second quarter on which interest will be provided.

Hope you understood the logic, now your answer is rate is 12% with quarterly compounding it becomes 12%/4 = 3% or 0.03 per quarter, 10 years becomes the 10 x 4 = 40 Quarter period.