KENTUCKY CROSSWORDS

Consumer Investments

The Power of Compounding and the Time Value of Money

The yield to maturity, a common term in bond investments is also what economists mean when they use the term "interest rates" and a simple definition for yield to maturity (YTM) used in this sense can be: the rate of return investors earn. The YTM can grow significantly through the power of compounding, (the process of determining a future amount based on original principal and accrued interest).

Rate of return coincides with the time value of money, which can be determined using the simple formula: FV = PV (1+i), where FV is the Future Value, PV is the Present Value; "1" adds in the original amount and "i" = interest rate.

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To see how the time value of money and the power of compounding can work, here is an example using amounts easy to calculate, $1000 invested in an account that pays 5% interest one time annually.

FV = PV (1+i)
FV = 1000 (1+0.05)
FV = 1000 (1.05)
FV = 1050

If we leave our balance after one year to earn interest for a second year, we get:
FV = PV (1+i)
FV = 1050 (1+0.05)
FV = 1050 (1.05)
FV = 1102.50

Thus we earned $52.50 in the second year, as opposed to the $50.00 earned in the first year.

Now let's examine the power of compounding in a bit more detail.

To determine the future value of an invested/deposited amount the formula for calculation is modified only slightly: FV = PV (1+i)ⁿ where n = the number of times the balance is compounded.

We'll leave our original $1000 to draw interest for 20 years at 5% compounded one time yearly and see what we get:
FV = 1000 (1.05)²⁰
FV = 2653.30

We earn almost 33% more (.3265 to be exact) on the balance by compounding; because if we had taken the interest payment out every year we would have received $50 yearly X 20 years = 1000, for a total of $2000.00.

Let's leave our original deposit of 1000 and leave it for 20 years but up the interest rate one percent to a 6% yearly return:
FV = 1000 (1.06)²⁰
FV = 3207.13

Our original deposit more than triples at this rate: 3207.13 - 2653.30 = 553.83.

We earned 55% more on our original deposit over a 20-year period by having a 1% higher interest rate. An obvious example of the importance of the rates in YTM.

Many bank deposits in interest bearing accounts are compounded quarterly. To calculate the balance above over the same time period at the same interest rate, we simply change the exponent (n in the formula above) to reflect the number of periods the interest is compounded.

For instance, compounded quarterly, n = 4 X 20; semiannually n = 2 X 20; monthly n = 12 X 20, and et cetera.

We then divide "i" by the same number; for quarterly 4; semiannually 2; monthly 12; where our formula looks like this: FV = PV (1 + i/t)^nt

Where
FV = the future value of our original investment
PV = Present Value (the original amount invested)
i = the annual interest rate
n = the number of years we leave our original investment to earn interest
t = the number of times interest is compounded in one calendar year.

The power of compounding is substantial. However, as we can clearly see from the simple examples given above, over an extended period of time we can earn more interest on interest than we can our original investment.

Disclaimer: Information on this Web site is intended for consumer informational purposes only.