Question

a) If the rate of interest is 10% p.a. and the interest is compounded
semi-annually, then the rate of interest computed per conversion
period(n) is ​

Answer 1

Answer:

COMPOUND INTEREST

Bank deposits, over time, usually have compound interest . That is, interest is computed on an account such as a savings account or a checking account and the interest is added to the account. Because the interest is added to the account (the alternative would be to mail the interest to the customer), the interest itself earns interest during the next time period for computing interest. This is what is meant when it is said that the interest compounds . See Salas and Hille, page 448-449.

The time interval between the occasions at which interest is added to the account is called the compounding period . The chart below describes some of the common compounding periods:

Compounding Period Descriptive Adverb Fraction of one year

1 day daily 1/365 (ignoring leap years, which have 366 days)

1 month monthly 1/12

3 months quarterly 1/4

6 months semiannually 1/2

1 year annually 1

The interest rate, together with the compounding period and the balance in the account, determines how much interest is added in each compounding period. The basic formula is this:

the interest to be added = (interest rate for one period)*(balance at the beginning of the period).

Generally, regardless of the compounding period, the interest rate is given as an ANNUAL RATE (sometimes called the nominal rate) labeled with an r. Here is how the interest rate for one period is computed from the nominal rate and the compounding period: