interest concepts.docx

Interest is defined as the cost of borrowing money, and depending on how it is calculated, can be classified as simple interest or  or compound compound interest. Simple interest is calculated on the principal principal,, or original, amount of a loan. Compound interest is calculated on the principal amount and also on the accumulated interest of previous periods, and can thus b e regarded as “interest on interest.” (For related reading, check out 7 Unconventional Ways Businesses Can Borrow Money .) There can be a big difference in the amount of interest payable on a loan if interest is calculated on a compound rather than simple basis. On the positive side, the magic of compounding can work to your advantage when it comes to your investments and can be a potent factor in wealth creation. While simple and compound interest are basic financial concepts, becoming thoroughly familiar with them will help you make better decisions when taking out a loan or making investments, which may save you thousands of dollars over the long term.

Basic Practical Examples Simple Interest

The formula for calculating simple interest is: Simple Interest = Principal x Interest Rate x Term of the loan =Pxixn Thus, if simple interest is charged at 5% on a $10,000 loan that is taken out for a three-year period, the total amount of interest payable by the borrower is calculated as: $10,000 x 0.05 x 3 = $1,500. Interest on this loan is payable at $500 annually, or $1,500 over the three-year loan term. Compound Interest

The formula for calculating compound interest in a year is: Compound Interest = Total amount of Principal and Interest in future (or Future Value) less Principal amount at present (or Present (or  Present Value) Value) = [P (1 + i) n] – P = P [(1 + i) n – 1] where P = Principal, i = annual interest rate in percentage terms, and n = number of compounding periods for a year.

Continuing with the above example, what would be the amount of interest if it is charged on a compound basis? In this case, it would be: $10,000 [(1 + 0.05) 3 – 1] = $10,000 [1.157625 – 1] = $1,576.25. While the total interest payable over the three-year period of this loan is $1,576.25, unlike simple interest, the interest amount is not the same for all three years because compound interest also takes into consideration accumulated interest of previous periods. Interest payable at the end of each year is shown in the table below.

Compounding Periods When calculating compound interest, the number of compounding periods makes a significant difference. Generally, the higher the number of compounding periods, the greater the amount of compound interest. So for every $100 of a loan over a certain period, the amount of interest accruedat 10% annually will be lower than interest accrued at 5% semi-annually, which will, in turn, be lower than interest accrued at 2.5% quarterly. In the formula for calculating compound interest, the variables “i” and “n” have to be adjusted if the number of compounding periods is more than once a year. That is, within the parentheses, “i” has to be divided by "n," number of compounding periods per year. Outsid e of the parentheses, “n” has to be multiplied by "t," the total length of the

investment. Therefore, for a 10-year loan at 10%, where interest is compounded semi-annually (number of compounding periods = 2), i = 5% (i.e. 10% / 2) and n = 20 (i.e.10 x 2). To calculate total value with compound interest, you would use this equation: = [P (1 + i/n) nt] – P = P [(1 + i/n) nt – 1] where P = Principal, i = annual interest rate in percentage terms, n = number of compounding periods per year, and t = total number of years for the investment or loan. The following table demonstrates the difference that the number of compounding periods can make over time for a $10,000 loan taken for a 10-year period.

Compounding Frequency

No. of Compounding Periods

Values for i/n and nt

Total Interest

 Annually

1

i/n = 10%, nt = 10

$15,937.42

Semi-annually

2

i/n = 5%, nt = 20

$16,532.98

Quarterly

4

i/n = 2.5%, nt = 40

$16,850.64

Monthly

12

i/n = 0.833%, nt = 120

$17,059.68

Associated Concepts In this section, we introduce some basic concepts associated with compounding. Time Value of Money Since money is not “free” but has a cost in terms of interest payable, it follows that a dollar

today is worth more than a dollar in the future. This concept is known as the time value of money and forms the basis for relatively advanced techniques like discounted cash flow (DCF) analysis. The opposite of compounding is known as discounting; the discount factor can be thought of as the reciprocal of the interest rate, and is the factor by which a future value must be multiplied to get the present value. (For more, see Understanding the Time Value of Money .) The formulae for obtaining the future value (FV) and present value (PV) are as follows: FV = PV (1 +i/n)  nt and PV = FV / (1 + i/n)  nt For example, the future value of $10,000 compounded at 5% annually for three years: = $10,000 (1 + 0.05) 3 = $10,000 (1.157625) = $11,576.25. The present value of $11,576.25 discounted at 5% for three years: = $11,576.25 / (1 + 0.05) 3 = $11,576.25 / 1.157625 = $10,000

The reciprocal of 1.157625, which equals 0.8638376, is the discount factor in this instance. The Rule of 72

The Rule of 72 calculates the approximate time over which an investment will double at a given rate of return or interest “i,” and is given by (72 / i). It can only be used for annual

compounding. For example, an investment that has a 6% annual rate of return will double in 12 years.  An investment with an 8% annual rate of return will double in 9 years. Compound Annual Growth Rate (CAGR)

The compound annual growth rate (CAGR) is used for most financial applications that require the calculation of a single growth rate over a period of time. For example, if your investment portfolio has grown from $10,000 to $16,000 over five years, what is the CAGR? Essentially, this means that PV = -$10,000, FV = $16,000, nt = 5, so the variable “i” has to be calculated. Using a financial calcu lator or Excel spreadsheet, it can be shown that i = 9.86%. (Note that according to cash flow convention, your initial investment (PV) of $10,000 is shown with a negative sign since it represents an outflow of funds. PV and FV must necessarily have opposite signs to solve for “i” in the above equation).

Present value (PV) and future value (FV) measure how much the value of money has changed over time. L E A R N I N G O B J E C TI V E  

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Discuss the relationship between present value and future value

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The future value (FV) measures the nominal future sum of money that a given sum of money is "worth" at a specified time in the future assuming a certain interest rate, or more generally, rate of  return. The FV is calculated by multiplying the present value by the accumulation function. PV and FV vary jointly: when one increases, the other increases, assuming that the interest rate and number of  periods remain constant.  As the interest rate (discount rate) and number of periods increase, FV increases or PV decreases.

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discounting The process of finding the present value using the discount rate.  present value a future amount of money that has been discounted to reflect its current value, as if it existed today capitalization The process of finding the future value of a sum by evaluating the present value. FULL TEXT 

The future value (FV) measures the nominal future sum of money that a given sum of money is "worth" at a specified time in the future assuming a certain interest rate, or more generally, rate of return. The FV is calculated by multiplying the present value by the accumulation function. The value does not include corrections for inflation or other factors that affect the true value of money in the future. The process of finding the FV is often called capitalization. On the other hand, the present value (PV) is the value on a given date of a payment or series of payments made at other times. The process of finding the PV from the FV is called discounting.

PV and FV are related , which reflects compounding interest (simple interest has n multiplied by i, instead of as the exponent). Since it's really rare to use simple interest, this formula is the important one.

FV of a single payment The PV and FV are directly related.

PV and FV vary directly: when one increases, the other increases, assuming that the interest rate and number of periods remain constant. The interest rate (or discount rate) and the number of periods are the two other variables that affect the FV and PV. The higher the interest rate, the lower the PV and the higher the FV. The same relationships apply for the number of periods. The more time that passes, or the more interest accrued per period, the higher the FV will be if the PV is constant, and vice versa. The formula implicitly assumes that there is only a single payment. If there are multiple payments, the PV is the sum of the present values of each payment and the FV is the sum of the future values of each payment.

How do annuities work?  An annuity is a long term investment that is issued by an insurance company designed to help protect you from the risk of outliving your income. Through annuitization, your purchase payments (what you contribute) are converted into periodic payments that can last for life. Nationwide's annuities are flexible so you can choose one that enables you to: 

Invest a lump sum or invest over a period of time

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Start receiving payments immediately or at some later date

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Select a fixed, variable or indexed rate of return

Investing involves risk and may lose value. All guarantees and protections are subject to the claims paying ability of the issuing company, but the guarantees do not apply to any variable accounts which involve investment risk and possible loss of principal.

What type of annuity could fit into your investment plan? Whether your needs are immediate or long-term, you can choose the type of annuity whose features work for your situation: 

Variable  –  With a variable annuity, you choose investments and earn returns based on how those investments

 perform. You can choose investments that offer different levels of risk and potential growth, depending on your investment goals and tolerance for risk. Variable annuities are sold by prospectus. Before you invest, please read the prospectus carefully and consider the investment objectives, risks, charges and expenses of the annuity and its underlying investment options before you invest. Prospectuses for products and underlying investment options contain this and other important information. To obtain prospectuses, call your investment professional or the insurance company. 

Immediate  –  An immediate annuity is usually purchased with a lump-sum and guaranteed income starts almost

immediately. Your investment converts into a guaranteed stream of income that is irrevocable once payments  begin. In some situations, funds can be accessed, but some restrictions apply. 

Fixed –  With fixed annuities, the principal investment and earnings are both guaranteed and fixed payments are

made for the term of the contract. 

Fixed Indexed  –  This special class of annuities yields returns on contributions based on a specified equity-

 based index, such as the S&P 500. A fixed indexed annuity offers returns based on the changes in a securities index, such as the S&P 500® Composite Stock Price Index. Indexed annuity contracts also offer a specified minimum which the contract value will not fall below, regardless of index performance. After a period of time, the insurance

company will make payments to you under the terms of your contract. A fixed indexed annuity is not a stock market investment and does not directly participate in any stock or equity investment.

Annuities generally fall into two categories: deferred and income. Each works differently and offers unique advantages.

Tax-deferred annuities: for retirement savings Deferred annuities can be a good way to boost your retirement savings once you've made the maximum allowable contributions to your 401(k) or IRA. 1 Like any tax-deferred investment, earnings compound over time, providing growth opportunities that taxable accounts lack. Deferred annuities have no IRS contribution limits, 2 so you can invest as much as you want for retirement. You can also use your savings to create a guaranteed 3 stream of income for retirement. Depending on how annuities are funded, they may not have minimum required distributions (MRDs). Bear in mind that withdrawals of taxable amounts from an annuity are subject to ordinary income tax, and, if taken before age 59½, may be subject to a 10% IRS penalty. Annuities also come with annual charges not found in mutual funds, which will affect your returns. Deferred variable annuities have funds that may have the potential for investment growth. However, this can involve some market risk and could result in losses if the value of the underlying investments falls. Variable annuities are usually appropriate for those with longer time horizons or those who are better able to handle market fluctuations. Some variable annuities allow you to  protect your investment against loss, while still participating in potential market growth. Deferred fixed annuities offer a guaranteed3 rate of return for a number of years. Fixed deferred annuities may be more suitable for conservative investors or for those interested in protecting assets from market volatility. In this way, they’re similar to certificates of deposit (CDs). However, deferred fixed annuities differ from CDs in that: Annuities are not FDIC-insured. Withdrawals from annuities prior to age 59½ may be subject to a 10% IRS penalty. Deferred fixed annuities may offer more access to assets than a CD. Annuity earnings compound on a tax-deferred basis. 

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Income annuities: for income in retirement Income annuities may be appropriate for investors in or near retirement because they offer guaranteed3 income for life or a set period of time. They may allow you to be more aggressive with other investments in your portfolio, since they provide a lifetime income stream. Keep in mind that you may have limited or no access to the assets used to purchase income annuities. Immediate fixed income annuities offer a guaranteed,3 predictable payment for life, or for a certain period of time. Your guaranteed income payment cannot be affected by market volatility, helping shield your retirement income from market risk. A cost-of-living increase is available at an additional cost to help your buying power keep pace with inflation. Deferred income annuities4 are fixed income annuities that have a deferral period before income  payments start. Because of the deferral period, you may get a higher income payment amount than

you would from a comparable immediate fixed income annuity with the same initial investment. The cost-of-living increase is also available at an additional cost for deferred income annuities.

Loading the player...  At some point in your life, you may have had to make a series of fixed payments over a period of time – such as rent or car payments  – or have received a series of payments over a period of time, such as bond coupons. These are called annuities. If you understand the time value of money, you're ready to learn about annuities and how their present and future values are calculated.

What Are Annuities?  Annuities are essentially a series of fixed payments required from you, or paid to you, at a specified frequency over the course of a fixed time period. The most common payment frequencies are yearly, semi-annually (twice a year), quarterly and monthly. There are two basic types of annuities: ordinary annuities and annuities due. 

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Ordinary annuity: Payments are required at the end of each period. For example, straight bonds usually pay coupon payments at the end of every six months until the bond's maturity date.  Annuity due: Payments are required at the beginning of each period. Rent is an example of annuity due. You are usually required to pay rent when you first move in at the beginning of the month, and then on the first of each month thereafter.

Since the present and future value calculations for ordinary annuities – and annuities due are slightly different – we will first discuss the present and future value calculation for ordinary annuities.

Read more: Calculating The Present And Future Value Of  Annuities http://www.investopedia.com/articles/03/101503.asp#ixzz4ncZsBfVf  Follow us: Investopedia on Facebook