Time value of money Given a choice, earning $100 today is preferable to earning $100 a year from now. If you earn $100 today, you can spend it or invest it. If you earn $100 a year from now, you must defer spending for a year. You also miss an opportunity to invest it.
This is an example of the time value of money, a very important concept in life, and a fundamental principle when it comes to budgeting, saving and/or investing. It is the economy that is said to determine the time value of money through the level of interest rates. Common interest rates for measuring the time value of money is the stated interest rate in a savings product, such as a CD, a fixed annuity, or treasuries. Let's call the $100 you can earn today the present value of a future amount. Let's call the amount you can earn in the future the future value. Interest rates connect present and future values. To be compensated for the time value of money, you require a certain interest rate.
It is the market that will determine the interest rate, relative to the time value of money in a free marketplace. This rate is determined by the interaction of demand and supply for funds in the economy. In the U.S., a 5% annual rate might be adequate compensation. In another country, where a higher rate of inflation erodes the future value of money, a 15% annual rate might be the market interest rate.
For example, if you deposit the $100 in a certificate of deposit (CD) that earns 5% annual interest, the future value in a year is $105. In this case, earning $105 a year from now may be enough to compensate you for not spending the $100 today. The $5 in interest represents the time value of money.
On the other hand, if the interest rate you require is higher, a 5% interest rate won't earn enough interest to compensate you. In this case, spending the $100 may have more value.
As you can see, the time value of money is determined by the level of market interest rates. If interest rates (and inflation) are low, the time value of money is relatively low. If interest rates are high, the time value of money is relatively high. The following table illustrates the time value of $100 at different interest rates for one and two years: | Years | 3.0% | 6.0% | 9.0% | 12.0% | 15.0% | | 1 | $97.09 | $94.34 | $91.74 | $89.29 | $86.96 | | 2 | $94.26 | $89.00 | $84.17 | $79.72 | $75.61 | | This is a clear example, as according to the chart above, $100 today would only be worth $94.34 a year from now if the market interest rate were 6%. Two years from now, $100 would only be worth $89, if the interest rate remained at 6%. Time value of money has many useful applications. One of the most important uses is that it helps you to measure the trade-off in spending and saving. This can have important consequences for your personal budgeting. If market interest rates are at 5%, you may decide that the time value of money is greater in the future, and decide to invest. If rates are a meager 2%, you may decide that the time value of money is higher today, and choose to spend. In general, all of this talk of present value and future value should make us think about future income needs and present savings habits. Next, we'll look at the power of compound interest. Benefits of compounding When you invest in savings instruments, CDs, fixed annuities, or fixed-indexed annuities, you earn interest at a contractual interest rate. The interest rate is usually stated as a yearly rate. For example, if you invest $1,000 in a certificate of deposit (a CD) that pays an annual interest rate of 5%, a year later you will have $1,050. The $50 in interest you earn in a year is your compensation for deferring consumption today.
If you decide to invest the $1,050 for another year at 5%, a year later you will have $1,102.65. In the second year, you earn $52.65 in interest, or $2.65 more than in the first year. This is because your investment is, in part, "earning interest on interest." This example illustrates a fundamental principle of saving and investing called compounding.
The following table shows the benefit of compounding on a $1,000 lump-sum investment. The investment is made for a range of interest rates and investment periods. For example, the table shows that $1,000 invested for three years at 6% grows to $1,181. These values are called future values, and these future values are rounded to the nearest dollar. The value is based on annual (once a year) compounding. We'll soon see the importance of compounding frequency on the future value of an investment: | Years | 4.0% | 6.0% | 8.0% | 10.0% | | 1 | $1,040 | $1,060 | $1,080 | $1,100 | | 3 | $1,125 | $1,191 | $1,260 | $1,331 | | 5 | $1,217 | $1,338 | $1,469 | $1,611 | | 10 | $1,480 | $1,791 | $2,159 | $2,594 | | Looking at the table, we see that $1,000 invested for 10 years at 6% has a future value of $1,791. Average interest earned each year on this investment is $79.10 [($1,791-$1,000)/10]. If the same investment were made for five years, average yearly interest declines to $67.60 [($1,338-$1,000)/5]. For three years, average yearly interest declines further to $86.70 [($1,260-$1,000)/3]. The higher average interest earnings reflect the benefit of compounding for a longer period of time. Logically, the more frequently you compound your investment, the greater the future value will be. While the table above shows the future values for investments that are compounded annually, financial institutions routinely compound your investments on a quarterly or monthly basis. Some financial institutions even offer continuous, or daily, compounding.
The following table reproduces the future values in the table above, only this time, the $1,000 investment earns interest that is compounded on a quarterly basis (four times a year): | Years | 4.0% | 6.0% | 8.0% | 10.0% | | 1 | $1,041 | $1,061 | $1,082 | $1,104 | | 3 | $1,127 | $1,196 | $1,268 | $1,345 | | 5 | $1,220 | $1,347 | $1,486 | $1,639 | | 10 | $1,489 | $1,814 | $2,208 | $2,685 | | As you can see, the increase in compounding frequency will increase the future values. The most dramatic increases occur at the highest interest rate and for the longest periods. In this example, from the top table, $1,000 that is compounded annually at 10% for 10 years is worth $2,594. Compounded quarterly, the same investment grows to $2,685. This is an extra $91 of interest you earn as a result of more frequent compounding. If the same investment is compounded daily, it grows to $2,720. This is an extra $126 in interest over annual compounding. Clearly, an increase in compounding frequency benefits the growth of your investment. Understand that compound interest is very different from simple interest.Simple Interest is calculated only on the principal, not on the principal plus the interest.If we were to review the previous example utilizing a beginning principal value of $1,000, and a 6% interest rate, over a 10 year time frame, you would have your original principal, plus interest of $6, but only $6, each and every year. The equitation would look like this: $1,000 + $60+ $60+ $60+ $60+ $60+ $60+ $60+ $60+ $60+ $60=1,600 Obviously, per our example we would rather earn $1,814 versus the simple interest result of $1,600. When it comes to repaying a loan, of course we would rather have to pay pack a borrowed sum based on a simple interest rate calculation, rather than a compounded one.
It will be advantageous to make additional contributions to your original investment as often as is possible. If you make regular contributions to your investment you will fuel its growth, producing a much larger future value.
The following table is a reproduction of the table, at top. In this case, the table shows future values for the original $1,000 investment, together with monthly contributions of $100 and monthly compounding. (Contributions are assumed to be made at the end of every period): | Years | 4.0% | 6.0% | 8.0% | 10.0% | | 1 | $2,263 | $2,295 | $2,328 | $2,361 | | 3 | $4,945 | $5,130 | $5,324 | $5,526 | | 5 | $7,851 | $8,326 | $8,838 | $9,389 | | 10 | $16,216 | $18,207 | $20,514 | $23,192 | | Future values begin to take off as a result of your making regular monthly contributions. For example, an initial investment of $1,000 and monthly contributions of $100, invested at 6% for five years, grows to $8,326. From the top table, we saw that a lump sum investment of $1,000 grows to a future value of $1,347. The difference in returns ($8,326-$1,347), or $6,979, represents the monthly contributions and the interest earned on the monthly contributions over the five year period. Since these contributions add up to $6,000 ($100*60), the $979 ($6,979-$6,000) is the total interest earned on the contributions. We've seen how compounding can boost the value of your investment. In general, the greater the frequency of compounding, the greater the future value of your savings. As you can plainly see, it pays to ask financial institutions to explain the rate of compounding that they use to either pay you interest on a deposit, or charge you interest on a loan. Triple Compounding (Tax-Deferred) Now we are going to talk about compounding, injecting taxation into the discussion. “Tax-deferred” means postponing your taxes on interest earnings until withdrawal at a future point in time. In the meantime, you are able to earn interest on your initial principal deposit, you earn interest on your interest, and you earn interest on the money you may otherwise have paid in taxes. You can accumulate more money over a shorter period of time, which will provide you with more savings, or a greater income. An annuity accumulates on a tax-deferred basis, as allowed by the IRS. A tax-deferred annuity is a contract between you and an insurance company for a guaranteed interest-bearing policy with guaranteed income options. The insurance company credits interest, and you don't pay taxes on the earnings until you make a withdrawal or begin receiving an annuity income. Your annuity contract earns a competitive return that is very safe. An annuity has a rate guarantee which is contractually part of every fixed annuity. Consumers have choices when it comes to the length of guarantee: CD or Multi-Year rate Guarantee Annuities, and Partial-Rate Guarantee Annuities.
Savings Advantages
Many people today are choosing tax-deferred annuities as the foundation of their overall financial plan. Consider that the traditional savings dollar may be taxed every year in products such as CDs or mutual funds. By postponing that tax with a tax-deferred annuity, your money compounds faster because you can earn interest on dollars that likely would have otherwise been paid to the IRS. Later, if you decide to take a monthly income, your taxes may be less because they will be spread out over a period of years. Similar to CDs, annuities have a penalty for early surrender. The slide above illustrates the reason people say, “It’s not what you earn, but what you keep”. Safety The safety that tax-deferred annuities provide a consumer is traditionally cited as the #1 reason consumers place their savings in tax-deferred annuities. Your tax-deferred annuity is safe because qualified legal reserve life insurance companies are required to meet their contractual obligations to you. Tax-deferred annuities protect your principal, your interest, and your ability to make withdrawals when you need income in retirement. There are independent rating services that examine the financial health of insurance companies such as A.M. Best, Standard and Poor’s, and Moody’s. Only insurance companies have the financial strength and the cash reserves to offer the guarantees found in an annuity. Mandated reserve requirements mean that when a tax-deferred annuity is purchased, the insurance company, by law, must set aside dollar-for dollar reserves to cover all anticipated payouts. We've also seen how making additional deposits adds discipline to your savings program and results in a much greater future value. The effect of consistent savings combined with tax-deferral can further enhance the size of your savings.
The above information is educational and should not be interpreted as financial advice. For advice that is specific to your circumstances, you should consult a financial or tax adviser.
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