How are exponential functions used to calculate compound interest

By Tayla Hamilton

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#1

- Compound interest is interest calculated on the initial principal, which includes all of the accumulated interest of previous periods of a deposit or loan.

(https://www.investopedia.com/terms/c/compoundinterest.asp)

- Compound interest can be calculated by using the exponential formula: FV = PV(1 + i)^N

FV = Future value (the amount you will have in the future)

PV = Present Value (the amount you have today)

i = Interest (your rate of return or interest rate earned)

N = Number of Years (the length of time you invest)

- This type of interest can be compounded on any frequency schedule which means that  

it can be continuous daily to annually.

- For example:

If you had a $5,000 loan with an annual 8% interest rate over a 4-year period then this is what each compounding period would look like:

#2

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*Investing: The act of committing money or capital to an endeavor with the expectation of obtaining an additional income or profit*

Investing is used by many as a way to set aside money and accumulate the results. When investing is used with compound interest, investments grow exponentially and can generate more return on your earnings. One can also invest into businesses, which is commonly known as investing into stocks. Buying shares from a stock gives the buyer the opportunity to own part of the company and participate in its success. It is important to note that diversification is key when buying shares of stocks since holding at least 2-3 can prevent 46% of your unsystematic risk.

Compound interest in business: Investing

Normally, businesses use compound interest as a way to open doors to sources of profits. Employers also use compound interest as a way to exclude a fixed amount of their employees' salaries and contribute it to their pension fund. This amount accumulates for years and the entire amount is given to them as their pension.

Another way that businesses use compound interest is when loans are used. For example, when a business decides to purchase an office building, many businesses choose to finance the transaction and take out a mortgage loan. With compounding, mortgage interest is charged to the principle and any previous interest that has already accumulated. Businesses can also choose to take out hard-money loans to help provide quick financing. Hard-money loans also have an interest that is calculated using compounding which means that the interest rate would be much higher than what is stated.

Compound interest in The Stock Market: Investing

Advantages Vs Disadvantages in The Stock Market: Investing

Advantages:

•As the economy grows, so does profit. This means that the ownership in stocks has an advantage in a growing economy.

•The stock market makes it easy to buy stocks as you can purchase them through a broker, a financial planner, or online.

•Stocks are easy to sell as you can sell them at anytime. This is important since it prevents the risk of being forced to take a loss in your investments.

Disadvantages:

•You could lose your entire investment if a company does poorly.

•A lot of time is needed to research the company you are buying into to determine how profitable you think they will be and if they will have success in the future.

•As stock prices rise and fall second by second, individuals have the tendency to buy high and sell low out of fear.

#3

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Credit Cards: The not-so-good form of interest

Credit cards are one of the most unavoidable starts to high interest. Credit cards typically have interest rates of 20% and even though they can be used as a short-term solution to help you pay off expenses, overtime they can become a pain if you fail to pay your balance. It is crucial to consider the reasons why you need a credit card before deciding to use one as it may cost you a lifetime amount of payments. The best reason for using a credit card is if you have urgent financial challenges such as medical bills or insurance. A better alternative to a credit card, however, is to use a personal loan which have fixed terms in order to help pay off the loan without the cycle of neverending repayments.

Savings accounts: The ultimate way to create good interest

The simplest and most common type of good interest is a savings account. Whether your savings account is big or small, overtime as the interest compounds, you will acquire good interest. Advantages of having a saving account is that it keeps your deposits separate from your other money in order for you to stop you from spending what you plan to save. As opposed to credit cards, there is no risk in having a savings account as you don't need to pay interest as the interest is gained to increase your investments in the long term.

#3

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The BIG controversy surrounding compound interest

During my research, I found that compound interest can become your enemy when you use loans since the increase in overall payment of a loan is due to the compounding interest. For example, if you only pay monthly on a credit card bill, the total can end up increasing substantially in which you would either end up paying a large amount more than the original purchase or the debt becomes impossible to get rid of. Because of this possibility, people have doubts and concerns about accumulating compound interest.

In Summary, exponential functions are used in:

Saving accounts

Stock

Interest Rates

Pensions

Loans

Compounding periods

Bibliography

• https://news.morningstar.com/classroom2/course.asp?docId=142858&page=2&CN=

• https://www.thebalance.com/stock-investing-for-the-individual-investor-3306182

• https://www.thebalance.com/the-power-of-compound-interest-358054

• https://smallbusiness.chron.com/uses-compound-interest-business-49709.html

• https://www.dividend.com/my-money/the-pros-and-cons-of-compound-interest/

• https://thecostaricanews.com/benefits-saving-account/

• https://www.pioneercreditconnect.com.au/tools-calculators/blog/2018/11/18/good-interest-bad-interest