Interest

From Wikicpa

Jump to: navigation, search

There are a variety of reasons which explain why lenders charge interest for the use of their money:

The time value of money: Most people would choose to have money in the present rather than money in the future. When asked to lend their current money in exchange for a promise to repay that money in the future, most lenders will agree only if they are repaid more than they originally lent. In effect, the interest rate is the payment for the use of money over time.

Alternative investments. The lender has a choice between using his money in different investments. If he chooses one, he forgoes the returns from all the others. In other words, lending incurrs an opportunity cost due to the possible alternative uses of the lent money.

Inflationary expectations. Most economies generally exhibit inflation, meaning a given amount of money buys fewer goods in the future than it will now. The borrower needs to compensate the lender for this.

Risks of investment. There is always a risk that the borrower will go bankrupt, abscond, or otherwise default on the loan. This means that a lender generally charges a risk premium to ensure that, across his investments, he is compensated for those that fail.

Liquidity preference. People prefer to have their resources available in a form that can immediately be exchanged, rather than a form that takes time or money to realise.

Taxes. Because some of the gains from interest may be subject to taxes, the lender may insist on a higher rate to make up for this loss.

1 Types of accrual
- 1.1 Simple interest
- 1.2 Compound interest
2 Also see

[edit]

Types of accrual

Most interest accrues (accumulates) as either simple interest or compound interest.

[edit]

Simple interest

Simple interest is interest that accrues linearly. In other words, it grows by a certain fraction of the principal per time period. Calculation of accrued interest of most debt uses simple interest. Once an interest payment is made, the lender can reinvest it elsewhere. In case they reinvest it in the original investment, interest will start accruing on this interest. In this case, they can calculate the growth of their investment using the compound interest method.

$A(t) = A_0 \cdot (1 + t \cdot r)\,$

$A (t)$ = Amount after $t$ years
$A 0$ = Principal (start amount)
$r$ = Interest rate
$t$ = Time in years

(Note: The interest rate is expressed as a pure decimal number (such as 0.06) rather than a percentage (such as 6%).

A(t) is called the amount function. The constant coefficient $A 0$ is usually dropped in mathematics of interest calculation, and the resulting accumulation function is used instead:

$a(t)=1+t \cdot r\,$

[edit]

Compound interest

Compound interest, previously called anatocism, is interest which is regularly added to the debt (compounded). Interest is then calculated not only over the principal, but also over the interest that has been added to the debt before--in other words, it is calculated over the total amount owed. With compound interest, the frequency of compounding influences the total amount of interest paid over the life of the loan. The amount function for compound interest is an exponential function in terms of time.

$A(t) = A_0 \left(1 + \frac {r} {n}\right) ^ {n \cdot t}$

$n$ = Number of compounding periods per year (note that the total number of compounding periods is $n \cdot t$ )

As $n$ increases the rate approaches an upper limit of $e r$ . This rate is called continuous compounding.

Many banks advertise an annual percentage yield (APY) which is the return on the principal over an entire year. For example, a 5% rate compounded monthly would have an approximate APY of 5.12%.

[edit]