# Does more frequent compounding result in additional return on the investment?

Asked on by yacel0762

lemjay | High School Teacher | (Level 2) Senior Educator

Posted on

Yes it does.

Interests with different compounding frequency can be compared with each other by determining their corresponding effective annual rate.

Using the formula of effective annual rate r,

r = [ 1 + (i/n)]^n - 1

r increases exponentially when the number of compounding periods, n, increases.

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To illustrate, let's try this problem.

John wants to invest his \$2000 on a plan. He receives two offers which are:

A - 10% annual percentage, compounded semi-annually

B - 10% annual percentage, compounded quarterly.

Among the two, which plan will give John a higher interest after 2 years?

Solution:

>> To determine which investment plan is better, calculate the effective annual interest of each.

For A,

r = [1+(i/n)]^n - 1 = [1+ (.10/2)]^2 - 1 = 1.05^2 - 1

r = 1.1025 - 1 = 0.1025 = 10.25%

Effective annual rate of A is 10.25%

For B,

r = [1+(i/n)^n - 1 = [1+(.10/4)]^4 - 1 = 1.025^4 - 1

r = 1.1038 - 1 = 0.1038 = 10.38%

Effective annual rate of B is 10.38%.

Since effective annual rate of B is greater than A, hence B is a better investment plan. B will yield a higher interest than A.

>> The other solution is by computing the future value of each plan after 2 years, using the compounding interest formula.

For A,

F = P [ 1 + (i/n)]^(nt)  = 2000 [ 1 + (.10/2)]^(2*2)

F = 2000(1.05)^4 =  2000(1.2155) = 2431

So, after 2 years, John money will increase from \$2000 to \$2431.  The total interest earned is \$431.

For B,

F = P [ 1+ (i/n)]^(nt) = 2000 [ 1 + (.10/4)]^(4*2)

F = 2000(1.025)^8 = 2000(1.2184) = 2436.8

John money will increase from \$2000 to \$2436.8. The total interest earned for 2 years is \$436.8.

Hence, plan B will give John a higher interest earned.

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Take note that in the above sample problem, B has a higher number of compounding periods than A. When solved, B yields a higher interest.

Thus, an increase in number of compounding periods in a year result to an additional return on investment.

Sources:

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