Question

Which of the following statements is correct, assuming positive interest rates and holding other things constant?

A) Banks A and B offer the same nominal annual rate of interest, but A pays interest daily and B pays semiannually. A deposit in Bank B will have a higher value in five years.

B) Banks A and B offer the same nominal annual rate of interest, but A pays interest quarterly and B pays monthly. A deposit in Bank B will have a higher value in five years.

C) Banks A and B offer the same annual rate of interest, but A pays interest quarterly and B pays semiannually. A deposit in Bank A will have a higher value in five years.

D) Banks A and B offer the same nominal annual rate of interest, but A pays interest weekly and B pays quarterly. A deposit in Bank B will have a higher value in five years

Answer 1

Solution:-

When two bank accounts pay the same rate of interest annually, it boils down to their compounding periods. The banks who pays interest more frequently during the year would ultimately yield higher value because of the effects of compounding.

In other words, when an interest payment is made, that interest gets added to the principal and the next interest is paid on the increased principal. So, the account that pays interest more frequently would add up paying more interest on interest than the bank that pays less frequently.

Further, please note that the nominal interest rates are after taking into account the effects of compounding. So, if the nominal interest rates offered by two banks are same, it means that the actual interest earned with two banks on annual basis would be same regardless of how the compounding periods differ among them. On the contrary, 'Annual interest rates' don't take into account the effect of compounding, so if two banks have same annual rate of interest but one pays interest more frequently, the annual interest earned through that bank will be higher due to more frequent compounding.

On the basis of above explanations, let's now look at all the options:

Option A: A and B have same nominal interest rates. It means that there value after 5 years would be same irrespective of frequency of compounding. Therefore, this option is not correct.

Option B: A and B have same nominal interest rates. It means that there value after 5 years would be same irrespective of frequency of compounding. Therefore, this option is not correct.

Option C: A and B have same annual rate of interest. However, A pays interest quarterly while B pays it semiannually. Further, this is the annual interest rate, i.e. prior to the effects of compounding. Since A pays more frequently, the value of A will be higher than B in 5 years due to effects of compounding. Therefore, this option is correct.

Option D: A and B have same nominal interest rates. It means that there value after 5 years would be same irrespective of frequency of compounding. Therefore, this option is not correct.

Hence, the correct options is option C.