Question

Bank accounts A and B have the same annual percentage interest. Account A pays interest monthly and B pays interest quarterly. If the same amount of money is deposited into both accounts, one year later, account A will generate more interest than B. True or False? Why?

Answer 1

True : Account A Will generate more interest than B

For Calculating Real Interest We have to consider the Effective Annual Interest

Effective Annual Interest = (1+ i/n)n - 1

Were i = Interest Rate

n = Number of Periods.

In Case of A its compuinding Monthly and in case of B its compouning Quarterly.

Say for Examble the Rate of Interest is 12 %

Effective Annual Interest in case of A = (1+ i/n)n - 1

i = 12%

n =12, since compounds monthly

Effective Annual Interest in case of A = (1+ 0.12/12)12 -1

=1.1268 -1

=12.68%

Effective Annual Interest in case of B = (1+ i/n)n - 1

i = 12%

n =4, since compounds Quarterly

Effective Annual Interest in case of B = (1+ 0.12/4)4 -1

Effective Annual Interest in case of B = 12.55%

Hence the more compounding in a year the more will be the interest Rate.

There fore Interest in A will be greater than B