Question

Which of the following statement(s) is/are most likely to be true?

I. If you were borrowing funds from a bank, and the quoted interest rate was 8% p.a., you would be better off if the bank used quarterly compounding rather than daily compounding.

II. If you were depositing funds at a bank and the quoted interest rate was 8% p.a., with interest compounded daily, you would be better off if the bank used a 360-day basis rather than a 365-day basis for compounding the interest rate

a) I only.

b) II only.

c) Both I and II.

Answer 1

First let us analyse each statement:

1. The rate of 8% is the nominal rate which is stated for the year. The actual rate at which interest gets accured is called the effective rate as it takes compounding frequency into account.

Effective rate

where i is the nominal rate per year & n is the number of compounding periods per year

The main point is that effective rate increases as the compounding frequency increases.

If the bank uses quarterly compounding, n=4 and effective rate will be less than daily compounding where n= 365.

So we will have to pay less interest in case of quarterly compounding. Thus the statement is TRUE.

2. This case is slightly different as the use of 360-day basis or 365-day basis only affects the daily interest rate, Interest will still be paid for actual number of days (365 for non leap years or 366 for leap years) in both the cases.

If the bank uses 360-day basis, daily rate will be 8%/360 which is greater than 8%/365. So we will get more interest every day. Thus this statement is also TRUE.

So the correct answer is C) Both 1 & 2

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