Continuous Interest

Explanation

Continuous interest is a form of compound interest. With continuous interest the length of the compounding period is reasoned to be infinitely small. The interest, therefore, is compounded continuously.

Formula

S	Final value of investment
P	Initial value of investment
r	Annual percentage rate (APR)
t	Number of years

Value of investment after t years:

S = Pe^rt

Where e is the transcendental number 2.7182818285...

Notice that the output, S, is an exponential function of t. That is, if we consider the final value of the investment as a function of the length of time for the investment, then t, the length of time for the investment, is in the exponent position, and this makes S an exponential function of it.

7) Prove that the simple interest is more profitable for investors than the compound interest rate if the

time of the deposit is less than a year and the interest rates are the same.

Смотри №4 про Simple and compound interest;

В доказательстве заменяем n>1 на n<1.

18. Effective and nominal interest rates. Inflation influence on interest rate.

The nominal interest rate is the periodic interest rate times the number of periods per year. For example, a nominal annual interest rate of 12% based on monthly compounding means a 1% interest rate per month (compounded). A nominal interest rate for compounding periods less than a year is always lower than the equivalent rate with annual compounding (this immediately follows from elementary algebraic manipulations of the formula for compound interest). Note that a nominal rate without the compounding frequency is not fully defined: for any interest rate, the effective interest rate cannot be specified without knowing the compounding frequency and the rate. Although some conventions are used where the compounding frequency is understood, consumers in particular may fail to understand the importance of knowing the effective rate.

Nominal interest rates are not comparable unless their compounding periods are the same; effective interest rates correct for this by "converting" nominal rates into annual compound interest. In many cases, depending on local regulations, interest rates as quoted by lenders and in advertisements are based on nominal, not effective interest rates, and hence may understate the interest rate compared to the equivalent effective annual rate.

The term should not be confused with simple interest (as opposed to compound interest) which is not compounded.

Interest rate is only meaningful in the context of time - in general is understood as - per year - which may be called

· the nominal interest rate

With other periods of time than year - like month, week, or day - the interest rate may be called

the effective interest rate ( The effective interest rate, effective annual interest rate, annual equivalent rate (AER) or simply effective rate is the interest rate on a loan or financial product restated from the nominal interest rate as an interest rate with annual compound interest payable in arrears.

It is used to compare the annual interest between loans with different compounding terms (daily, monthly, annually, or other). The effective interest rate differs in two important respects from the annual percentage rate (APR):^[1]

1. the effective interest rate generally does not incorporate one-time charges such as front-end fees;

2. the effective interest rate is (generally) not defined by legal or regulatory authorities (as APR is in many jurisdictions).)

Дата добавления: 2015-11-16