Simple Interest

Simple interest is a very basic way of looking at interest. The various methods used to calculate interest are basically variations of the simple interest calculation method. In fact, your interest – whether you’re paying it or earning it – is usually calculated using different methods The basic concept underlying simple interest is that interest is paid only on the original amount borrowed for the length of time the borrower has use of the credit. The amount borrowed is referred to as the principal. In the simple interest calculation, interest is computed only on that portion of the original principal still owed. The main limitation that you should keep in mind is that simple interest does not take compounding into account.

If you want to calculate simple interest, the general formula is:

Simple Interest ( I ) = P (principal) x R (annual interest rate) x N (years)

In other words Interest (I) is calculated by multiplying Principal (P) times the Rate (R) times the number of Time (N) periods.

For example, if you invest \$1,000 at a 6% annual interest rate for one year means that you would receive \$60 in interest (1000 x .06 x 1). Note: the interest rate, R, is converted to a decimal as .06 and not written as percent.

The formula can be simplified to calculate the total repayment, principal plus the accumulated interested.

TR ( total return ) = P (1 + N x R)

For example, if you invested \$1,000.00 at a simple interest rate of 7% for one year than you would receive a total of \$1070.00 or \$1000.00 ( 1 + 1x.07 ) = \$1070.00.

If we had an investment that lasted two years the total return, using simple interest, would be:

\$1000.00 ( 1 + 2 x .07 ) = \$1140.00.

This example is correct if the interest is paid at the end of the two-year term. There will be a significant change in the results if the interest is paid out during the term of the investment. In this case, the investor will have the option of reinvesting the interest that is paid.

Compound Interest

Compound interest is the concept of adding any accumulated interest back to the principal, so that interest is earned on the principal amount and the addiotnal interest from that time on. When your interest is compounded it means that it is added back to your original capital, from which point it then starts to earn interest itself. The bank is now paying you interest on the money they’ve paid you in interest. The process of making the interest to now be principal is called compounding the interest is compounded.

For example, if you invest \$1,000 at a rate of 5 percent per year, your initial investment is worth \$1,050 after one year. During the second year, assuming the same rate of return, earnings are based not on the original \$1,000 investment, but also on the \$50 in first-year earnings. Over time, compounding can produce significant growth in the value of an investment. So, the earlier you start investing, the faster your investments can grow in value.

Compound interest may be contrasted with simple interest, where the interest earned is not added to the principal and therefor there is no compounding. Compound interest predominates in finance and economics, and simple interest is used infrequently, although certain financial products may contain elements of simple interest.

Compound interest rates may be converted to allow for comparison: for any given interest rate and compounding frequency, an “equivalent” rate for a different compounding frequency exists.
Compounding methods are all based on the same formula to calculate the rate of return. However, the compounding period may be different on different products or between different institutions. Annual compounding would mean the interest rate is compunded yearly. Semi annual compounding has the interest compounded twice a year. Quarterly compounding would have the interest compounded four times a year or at the end of every quarter. Monthly compounding will have the interest compounded each month. Daily compounding has the interest compounded each day.

The greater the frequency of compounding in turn means a decrease in the amount of time before interest earns interest. The sooner the interest starts earning interest the more total interest will be earned. The shorter the time period is for the compounding, the better the terms are for the depositor. Compound interest helps your money grow faster and can be especially powerful when the interest rate paid is higher, the compound period is frequent and the time horizon for maintaining those components is longer.

Compound Interest Formula:

If you want to calculate simple interest, the general formula is:

A = P (1 + r/n)n

P is the principal
R is the annual rate of interest
N is the number of times per year the amount is compounded.
TR is the amount of money accumulated after n years, including interest or the total return.

When the interest is compounded once a year:

TR = P (1 + R)N

However, if you had a deposit for 5 years that is compounded once a year the formula will look like:

TR = P (1 + R)5

If you now have a deposit that compounds twice a year for five years the formula would like this:

TR = P (1 + R/5)5

Here is an example if you have an account where you deposited \$1000.00 and the bank compounds the interest twice a year at an interest rate of 5%.

TR = \$1000.00 ( 1 + .05/2 )2
TR = \$1050.63

This formula applies to both money invested and money borrowed.

Frequent Compounding of Interest:

What if interest is paid more frequently?
Here are a few examples of the formula:
Annually = P × (1 + R) = (annual compounding)
Quarterly = P (1 + R/4)4 = (quarterly compounding)
Monthly = P (1 + R/12)12 = (monthly compounding)
Daily compounding = Principal (1 + interest rate/365)365 = (daily compounded amount)

A one time investment of \$1000.00 paying an interest rate of 7% compounded monthly will have a total return of \$1,074,555.52 after 100 years. Compound interest is one of the most powerful growth forces in investment markets,whether it be money market funds, certificates of deposit or the accrued earnings of publicly traded corporations.

Rule of 72

In finance the rule of 72 is a method for estimating an investments doubling over time at a given interest rate or conversely a method of calculating at what interest rate it will take to double an investment for a set period of time. The rule of 72 provides quick estimated of calculating approximately how many years it takes an amount of money to double when it receives compound interest. The rule says you can find the answer by dividing the rate of interest, using a whole number for the interest rate and not a percent, for example, a 6% rate of interest equals 6, divided into 72. Thus, at 6% compound interest, a sum will double in about 12 years, 72 divided by 6. At 10% compound interest it will double in about seven years, 72 divided by 10.

Discount Method of Calculating Interest

When the bank discount calculation method is used, interest is calculated on the amount to be paid back, and the borrower receives the difference between the amount to be paid back and the interest amount. The bank discount method is also referred to as the discount basis.

Under the discount method, the interest that will be due is calculated and withheld from the borrower when the loan is made. For example, someone who borrows \$1,000 for a year at a 10% interest rate would actually receive just \$900 (\$1,000 minus 10% of \$1,000, or \$100), and then pay back \$1,000 a year later. The effective interest rate would thus exceed 11% (\$100 divided by the \$900 that the borrower had the use of during the year).

Suppose there is a government bond that sells for \$95 and pays \$100 in a year’s time. The discount rate represents the discount on the future cash flow:
The interest rate on the cash flow is calculated using 95 as its base:
For every interest rate, there is a corresponding discount rate, given by the following formula:

Accrued Interest

Accrued interest is a term often used in finance with regards to interest bearing assets. Accrued interest is interest earned but not yet paid on an interest bearing assets like a certificate of deposit or bond. Accrued interest represents that has been earned for a time period since that last interest paid date. If interest is paid monthly and the CD or bond is collected in the middle of a month, there will be interest accrued between the end of the previous month and the middle of month when the principal of the bond or CD was paid. Accrued interest can be calculated based on the interest rate being paid on the account and the number of days between the last interest payment date and either the day the account is settled or the next payment date.

As an example:

If a customer holds a \$1000.00 account that pays 6% interest on the 1st of the month, the last payment date was April 1st and the account matures on April 15, the accrued interest for April would be;

April 1 – April 15 = 14 days
\$1000.00 x 14/365 x .06 = \$2.30 in accrued interest

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