Compound interest and percentage

Compound Interest and percentages

Interest rate that is computed on the initial principal and as well on the accumulated interest of previous periods of a deposit or loan is known as a compound interest. Compound interest can be described in order words as “interest on interest,” and will make a deposit or loan grow at a faster rate than simple interest, which is interest computed just on the principal amount.

The rate at which compound interest accumulates depends on the frequency of compounding; the greater the number of compounding periods, the greater the compound interest. Therefore, the amount of compound interest accumulated on N100 compounded at 10% every year will be smaller than the one on N100 compounded at 5% semi-yearly over an equivalent period of time. Compound interest is as well referred to as compounding.

Compound interest is interest added to the principal of a deposit or loan in order that the added interest as well earns interest from then on. This addition of interest to the principal is referred to as compounding. A bank account, for instance, may have its interest compounded every year: in this case, an account with N1000 starting principal and 20% interest every year would have a balance of N1200 at the end of the first year, N1440 at the end of the second year, N1728 at the end of the third year, etc.

To completely define an interest rate, permitting comparisons with other interest rates, both the interest rate and the compounding frequency ought to be known. Due to the fact that the majority of people preferably consider rates as a yearly percentage, a lot of governments need financial institutions to mention the equivalent yearly compounded interest rate on deposits or advances. For example, the yearly rate for a loan with 1% interest per month is roughly 12.68% every year (1.0112 − 1).

This identical annual rate may be known as annual percentage rate (APR), annual equivalent rate (AER), effective interest rate, effective annual rate, and other terms. When a fee is charged up front to get a loan, APR normally counts that cost in addition to the compound interest in converting to the equivalent rate. These government requirements help consumers in making comparisons to the real costs of borrowing more readily.

For any given interest rate and compounding frequency, an identical rate for any different compounding frequency is available.

Compound interest may be distinguished from simple interest, where interest is not added to the principal (there is no compounding). Compound interest is typical in finance and economics, and simple interest is used once in a blue moon despite the fact that particular financial products may be made up of elements of simple interest.

Compound Interest'

The formula for calculating compound interest is:

Compound Interest = Total amount of Principal and Interest in future (or Future Value) smaller Principal amount at present (or Present Value)

= [P (1 + i)n] – P

= P [(1 + i)n – 1]

(Where P = Principal, i = nominal annual interest rate in percentage terms, and n = number of compounding periods.)

If the number of compounding periods is more than once a year, "i" and "n" ought to be adjusted correspondingly. The "i" ought to be divided by the number of compounding periods per year, and "n" is the number of compounding periods per year multiplied by the loan or deposit’s maturity period in years.

For instance:

• The compound interest on N10,000 compounded yearly at 10% (i = 10%) for 10 years (n = 10) would be = N25,937.42 - N10,000 = N15,937.42

• The amount of compound interest on N10,000 compounded semi-annually at 5% (i = 5%) for 10 years (n = 20) ought to be = N26,532.98 - N10,000 = N16,532.98

• The amount of compound interest on N10,000 compounded monthly at 10% (i = 0.833%) for 10 years (n = 120) would be = N27,070.41 - N10,000 = N17,070.41

Compound interest can greatly enhance investment returns over the long term. Whereas a N100,000 deposit that receives 5% simple interest ought to earn N50,000 in interest over 10 years, compound interest of 5% on N10,000 ought to grow to $62,889.46 over an equivalent period of time.

Whereas the magic of compounding has resulted to the fictional story of Albert Einstein apparently calling it the eighth wonder of the world and/or man’s greatest invention, compounding can as well work against consumers who have loans that are attached with very high interest rates, like credit-card debt. A credit-card balance of N20,000 carried at an interest rate of 20% (compounded monthly) Would amount to total compound interest of N4,388 over one year or roughly 365 per month.

Comparing Simple Interest To Compound Interest

Compound interest is based not just on the original sum, but as well on accrued interest. For instance, many credit cards charge compound interest every month. If you borrow N1,000 with a simple annual interest rate of 12 percent, you pay less in interest than if you borrow an equivalent amount with a compound interest rate of 1 percent per month. If the loan with the simple interest is paid off at the end of the year, the total amount in interest paid is N120. Nevertheless, with the compound interest, it costs N126.83.

The reason is that, much different from simple interest, compound interest builds upon itself monthly. Despite the fact that the difference is just 6.83 in the above example, the majority of people witness a far more striking variation. Since the majority of credit cards have compound interest rather than simple interest and a lot of people pay just the minimum amount on their credit card payments, the interest adds up very quickly.

Compound Interest Formula

Compound interest which means that the interest you earn every year is added to your principal, in order that the balance doesn't merely grow, it grows at an increasing rate - is one of the most essential concepts in finance. It is the basis of everything from a personal savings plan to the long term growth of the stock market. It as well accounts for the effects of inflation, and is significant during the payment of debt.

The effect of compounding depends on the frequency with which interest is compounded and the periodic interest rate which is used. Thus, to correctly define the amount to be paid under a legal contract with interest, the frequency of compounding whether it is annually, half-annually, quarterly, monthly, daily, and so on and the interest rate ought to be made known. Different laws may be applied depending on the country as different countries have different law guiding this procedure. In finance and financial institutions however, the most common occurrence are the following:

The periodic rate is the amount of interest that is charged (and afterward compounded) for every one of the periods divided by the amount of the principal. The periodic rate is mainly used p for calculations and is scarcely used for comparison.

The nominal annual rate or nominal interest rate is the periodic rate times the number of compounding periods every year. For instance, a monthly rate of 1% is the same as the annual nominal interest rate of 12%.

The effective annual rate is the total compounded interest that would be payable up to the end of a single year divided by the principal.

Economists in general prefer to make use of efficient annual rates to simplify comparisons, but in finance and commerce, the nominal annual rate may be specified. When specified in addition to the compounding frequency, a loan with a specific nominal annual rate is completely specified (the amount of interest for a given loan situation can be accurately calculated, but the nominal rate cannot be unswervingly compared with that of loans that possesses a different compounding frequency.

Loans and financing may possess charges other than interest, and the terms above do not try to embrace these disparities. Other terms like the annual percentage rate and annual percentage yield may be composed of a particular legal definitions and may or may not be comparable, depending on the jurisdiction.

The use of the terms explained above (and other related terms may be incoherent and differ from country to country depending on the local custom or marketing demands, for straightforwardness or for other reasons.

There are a few exceptions like the:

US and Canadian Short term Government debt. These have a different convention. Their interest is computed as (100 − P)/Pbnm,[ where P is the price paid. Instead of normalization for a year, the interest is prorated by the number of days t: (365/t)×100.

The interest on corporate bonds and government bonds is normally payable twice yearly. The amount of interest paid every six months is the specified interest rate divided by two and multiplied by the principal. The annual compounded rate is higher than the disclosed rate.

Canadian mortgage loans are in general compounded semi-annually with monthly or more regular payments.

U.S. mortgages make use of an amortizing loan, not compound interest. With these loans, an amortization schedule is employed to determine how to apply payments toward principal and interest. Interests accumulated on these loans is not added to the principal, but instead are paid off every month when the payments are applied.

It is oftentimes mathematically easier like in the valuation of derivatives, to make use of continuous compounding, which is the limit as the compounding period gets to zero. Continuous compounding in pricing these instruments is a natural result of Itō calculus, where financial derivatives are valued at ever increasing frequency, till such a time the limit is got to and the derivative is valued in continuous time.

Percentage

What is a percentage?

Percent means “for every 100” or "out of 100." The (%) symbol as a handy way to write a fraction with a denominator of 100. For instance, rather than saying "it rained 14 days out of every 100," we say "it rained 14% of the time."

Percentages can be written as decimals by moving the decimal point two places to the left:

Decimals can be written as a percentages by moving the decimal point two places to the right:

Formula for estimating percentages

The formula for estimating percentages or for converting percentages are more or less simple.

To convert a fraction or decimal to a percentage, multiply by 100:

To convert a percentage to a fraction, divide by 100 and reduce the fraction if need be.

Examples of percentage calculations

Below are two examples to illustrate how to calculate percentages.

1) 12 people out of a total of 25 were female. What percentages were female?

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2) The price of a N1.50 candy bar was to be increased by 20%. What was the new price?

3) The tax on an item is N6.00. The tax rate is 15%. What is the price without tax?

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