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*Comprehensive Study on Interest Rates and Discount
Rates*

1.
Interest Rates are the Fundamental Part of the Actuarial Work.

2.
In What Situations will Banks act as a Borrower?

- accepts money from savers

- issues own shares to investors

- it sells Fixed interest Securities

*So,
how does a lender charge interest rates. Let’s see 2 Scenarios:*

__Scenario
1: __If you lend money
to US government and to a Businessman, then you will probably demand a higher
rate of interest from businessman as he is more likely not to repay the loan or
interest amount.

__Scenario
2: __If
a lender expects higher inflation over the term of loan, it may demand higher
rate of interest to increase its real return

*INTEREST:*

1.Simple
Interest: Here the interest once credited, does not itself earn further
interest. So, the **accumulation factor will be: (1+ni) **= here “n”
represents no. of years and “i” represents simple interest rate per annum.

*This
is not the right approach that further interest rate is not earned on earlier
interest because you as an investor withdraws your money with interest and then
invest somewhere to get more return. Even by using this technique it leads to
heavy and unnecessary additional transaction expenses. Let’s see an example:*

*a.)I
invested 1000rs today at 10% p.a. for 2 years simple interest. My amount at the
end will be rs.1200*

*b.)I
invested 1000rs today for 1 year at 10%p.a. and I will get after 1 year rs.1100
and then reinvested rs.1100 again for one more year and get rs.1210.*

__Then
there comes Compound Interest:__

2.Compound
Interest: Here the interest itself earns interest. So **accumulation factor will be: (1+i)**^{n}^{
}where “i” represents compound interest rate

**Principle of
Consistency (From Accumulation Context): A(t**_{0 , }t_{n}) = A(t_{0,}t_{1})*A(t_{1},t_{2})…..*A(t_{n-1,}t_{n})

Important
point: Nominal rates are those where interest rates are paid more frequently
than once per unit time. Bank accounts normally use nominal rates. They quote
the annual interest rate but interest is actually added at the end of each
month. Thus, here interest is paid more frequently than once per unit time
year.

*DISCOUNT:*

1.Simple
Discount: **Accumulation
factor will be (1-nd).**

2.
Compound Discount: **Accumulation Factor will be (1-d)**^{n}
.

Where
is simple discount rate used normally? = It is often quoted for treasury bills
which are short term loans made by the government. Rather than quoting the
amount they wish to borrow they quote the amount of repauyment.

Let’s
revise now the accumulated values using accumulation factors:

Simple
interest= P(1+ni) = A

Compound
Interest = P(1+i)^{n} = A

Simple
Discount = A(1-nd) = P

Compound
Discount = A(1-d)^{n} = P

So,
what is the difference between interest rate and discount rate? = Discount rate
is interest paid at the start of the year. Interest rate is the interest that
is paid at the end of the year.

Example=
I have Rs. 100 to invest *@10% interest rate p.a.* Then I will
get Rs.110 at the end of the year. Now I
want 100Rs. Loan at *10% discount rate p.a. *Then in this case I will get Rs.90 in
the beginning and I have to pay Rs.100 at the end of the year.

*Case
Study Question: *If
you are a borrower and go to bank for a loan of rs.100. Now banker say that you
have 2 choices that either you can get the loan at 10% discount rate or get the
loan at 10% interest rate. So, which option will you choose and why?

*Case
Study Answer:*
As a borrower I will choose to get loan at 10% interest rate because when I
convert 10% discount rate into interest rate it will be more than 10% interest rate;
and as a borrower I am looking for loan at minimum interest rate.

Last
point : We can equate two rates using their accumulation factors. For
reference, see ch-2 of CT1.

*Follow me on LinkedIn: Kamal Sardana*

Please Explain mathematically your case study answer.

ReplyDeleteRefer CT1 book or read another article where the formula is given

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