BOARD CERTIFICATION EXAM STUDY GUIDES Lower Extremity Trauma
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In the case of financial investments, compounding interest relies on time to reveal its true magic.
Here’s how: a young investor can invest less money over a longer period of time than an older investor who invests more money over a shorter period and ends up with more in the end. Compounding returns grow exponentially, making time more than an ally – but a force of the universe driving growth.
Time is certainly our ally in investing, but according to ME-P Editor Dr. David Edward Marcinko MBA MEd, you’ll kick yourself wishing you had invested earlier when you witness compounding after a few years (or a decade).
Marketability and liquidity are two concepts that are interrelated but often confused by the medical professional. Marketability deals with the speed at which an asset can be turned into cash. Liquidity, on the other hand, deals with an asset that can be turned to cash without a significant loss of value. A physician’s practice may still be good investment, but is it not particularly marketable or liquid. A common stock traded on the New York Stock Exchange can be easily sold for its quoted fair market value.
[B] The Time Value of Money
To the young physician starting a career, the time value of money is not a primary concern. It involves spending dollars in the future compared with spending today. Paying off high student loans while earning a relatively low salary leaves barely enough for present personal consumption. In the past, the rationale to spend today, forsaking the future, was not only a function of necessity but stemmed from the probability that future income would grow appreciably higher. Today, this is no longer a given for medical professionals.
In the simplest terms, a dollar today is worth more than a dollar tomorrow. The supply and demand for a dollar today to be paid back in the future is what determines interest rates. This calls for an understanding of the concepts of present and future value.
Present value is what you have today. So a dollar is a worth a dollar.Future value is what that dollar will grow to when compounded at a given interest rate. If you started with 100 dollars and earned 10 percent for five years, you would end up with 161 dollars.
Year Paying Interest Ending Interest
Amount of Factor Amount (annual)
1 $ 100 1.10 $ 110.00 $ 10.00
2 110 1.10 121.00 11.00
3 121 1.10 133.10 12.10
4 133.10 1.10 146.41 13.31
5 146.41 1.10 161.05 14.64
$ 61.05
Whenever you do not have a financial calculator, such as a Hewlett-Packard 12-C, Texas Instruments BA III plus, apps, SAAS, or computer spreadsheet or handy, you can figure future value with this formula.
FV = PV (1 + i)^N
FV is future value and PV is present value. The periodic interest rate is represented by the i. The number of periods being compounded is the n. The N means to the power of some number. In the example above, the equation would appear as follows:
FV = $100(1+.1)^2
FV = $100(1.21)
FV = $121
N
Likewise, the formula for present value is: PV = amount / (1 + i )
Other time value of money concepts, easily determined with a calculator, or interest table include the future value of multiple (equal) cash flows (ordinary annuity); conversion to an annuity due; the present value of multiple (equal) cash flows (ordinary annuity); and the conversion to an annuity due.
Example: Determining a Funding Amount
Dr. Smith has a daughter who plays the piano very well. He wishes to accumulate funds for his daughter Mackenzie’s advanced music education. He estimates that she will need $6,000 per year in today’s dollars, and will start school at age 18. She is 10 years old now. Costs are expected to increase 6 percent annually. Dr. Smith and his financial advisor believe that he can earn 9 percent after tax on his funds. How much is required?
Step # 1: Determine the future value of $6,000, 8 years from now. Or, what will Mackenzie’s first-year piano school cost, considering inflation?
Using a financial calculator, such as the HP 12-C: @ 8n (years), 6i (interest rate); $ 6,000 PV; the future value is $9,563
Step # 2: Next, determine the lump sum necessary to provide the above amount at the start of each year (present value annuity due).
Again, using the HP12-C @ $9,563 PMT; g7 (PVAD); 4 N; 1.09/1.06 i; the present value is $36, 702.
Step # 3: Compute the annual savings required at the end of each year (ordinary annuity) to provide the lump sum needed at age 18.
Finally, calculate with the HP 12-C @ g8 (ordinary annuity); $ 36,702 FV; 8N; 9i, and solve for PMT = $ 3,328.
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