Question

Comparing Rates: The Effect of Compounding-

1- In general, what is the relationship between a stated interest rate and an effective interest rate? Which is more relevant for financial decisions?

2- What does continuous compounding mean?

Loan Types and Loan Amortization

3-What is a pure discount loan? An interest-only loan?

4-What does it mean to amortize a loan?

5-What is a balloon payment? How do you determine its value?

Answer 1

1 The effective interest rate shows the actual interest rate revived on the investment over the period based on the number of compounding. The higher the number of compounding , the more will be the effective interest rate realized on the investment.

Thy are related as

EIR = (1+ i/m)^m -1

Where

EIR = Effective rate of interest %

I = Nominal or the stated rate %

M= no of compounding in a year

The Effective interest rate is more relevant in the making of financial decisions because it shows the rate at which our investment actually grows over the period of time taking into consideration all the compounding factor .

2 In continuous compounding the interest rate on the investment is compounded for infinite number of times theoretically. Therefore the accrued interest is compounded back into the investment for infinite number of times .

It is estimated as a exponential power of rate and time as   e ^ (rt )

3. In a pure discount loan a certain and fixed corpus money contracted at the time of initiation of the loan .,, needs to be paid at the end of the loan tenure in order to pay off the loan. This type of loan doesn’t involve any time of regular interest and principal payment in form of instalments in order to gradually pay off the loan. The whole loan amount is paid p off by a single payment at the end of the loan period

In the interest only loan, a special provision is allowed to the borrower to pay off only the accrued monthly interest s on the loan for a fixed amount of the time. The loan principal remains unchanged and only the interest obligation s during the period is paid off .

4 Amortizing a loan means gradually paying off or reducing the balance outstanding on the loan by a equal and regular payments at intervals know as the instalment payment of the loan . Amortizing takes into account both the interest accrued in the period and a part of principal to be paid off in each instalment period . This gradually pays off the liability outstanding

5. balloon payment is a special type of loan payment mainly used for the mortgage category of the loans which involves a large payment in the ending to completely pay off the loan .

The balloon payment is determined by

Payment balloon = (PV- balloon Amount /(1+r)^n) x( r/(1-(1+r)^-n

Where

PV = The present value of the loan

R = rate of interest

R = ROI %

Thanks