What is rounding?

Rounding a number means approximating it. A rounded number is often easier to use, understand, and remember than the precise number. In MyFinanceLab most of our answers are rounded decimal numbers. A decimal number has three parts: The whole number part, the decimal point and the decimal part.

For example: [pic]

So, in order to round a decimal number we basically round the decimal part of it.

These are the two basic steps for rounding decimals to a place value to the right of the decimal point
Step 1: Locate the digit to the right of the given place value.
Step 2: If this digit is 5 or greater, add 1 to the digit in the given place value and delete all digits to its right. If this digit is less than 5, delete all digits to the right of the given place value.

For example: Round 736.2359 to the nearest hundredth.
Solution:
Step 1: We locate the digit to the right of the hundredths place
Step 2: Since the digit to the right is 5, we add 1 to the digit in the hundredths place and delete all digits to the right of the hundredths place.

Thus, 736.2359 rounded to the nearest hundredth is 736.24

Rounding in MyFinanceLab
In MyFinanceLab we use input instructions to indicate the place value to which you must round your final answer(s).

For example: Let’s say your final answer is 736.2359. • You must enter 736.2 if the input instruction is: Round to the nearest tenth. • You must enter 736.24 if the input instruction is: Round to the nearest hundredth. Note: Other typical input instruction in MyFinanceLab is Round to the nearest cent if the final answer is in currency units. • You should enter 736.236 if the input instruction is: Round to three decimal places.

Now, let’s use a simple Time Value of Money (TVM) question you may encounter in MyFinanceLab.
| |
|Problem Example: Comparing Interest for Various Compounding Periods. If $1,000 is invested at 8% compounded |
|annually, |
|monthly, |
|what is the amount after 5 year? (Round to the nearest cent.) |

To solve this problem without using a financial calculator or a spreadsheet, we need to use the compound interest, future value, formula:

[pic] where, |i |= |r/m |
|FV |= |future value at the end of n periods |
|PV |= |present value |
|r |= |annual rate |
|m |= |number of compounding periods per year |
|i |= |rate per compounding period |
|n |= |Total number of compounding periods |

Solution: a. Compounding annually means that there is one interest payment period per year. So, n = 5 and i = r = 0.08.

[pic] [pic] [pic]

Therefore, rounded to the nearest cent, the final answer is $1,469.33

b. Compounding monthly means that there are twelve interest payments per year. So, n = 12(5) = 60 and i = 0.08/12 = [pic]

[pic] [pic]

Therefore, rounded to the nearest cent, the final answer is $1,489.85

| |
|This TVM example helps us to understand a basic rounding principle in MyFinanceLab: “Do not round until the final answer.” As you |
|can see in part a. after solving the expression [pic]we leave it unrounded and use as many digits as possible in its decimal part. |
|The same happens in part b with the other exponential expression. |
| |
|Take another look at part b. because rounding i to a small number of decimal places, such as 0.007 or 0.0067, would have resulted |
|in round-off errors. So, to avoid this, use as many decimal places as your calculator is capable of displaying. |

Tips:
If you want to calculate TVM problems, mathematical calculations are relatively straightforward. However, as you will see, TVM calculations are easier using a financial calculator or spreadsheet. But, no matter what method you use – equation, financial calculators, or spreadsheets, you get the same answer because they all use the same formula and concept. These are some tips for solving TVM questions.

Calculator Tips: • Set your calculator to display at least five decimal places or to floating decimal place (nine decimal places). • Set your calculator to one payment per year. Adjust this setting if necessary. • Set your calculator to the “end” mode. Adjust this setting if necessary.

Excel Tips: • Take advantage of the formula help that Excel offers. • If you are lost, click on “Help”. • Be careful about rounding variables. For example, suppose you’re dealing with the interest rate 6.99% compounded monthly. This means you will need to enter the interest rate per month, which is = 6.99%/12, and since you are performing division in the cell, you need to put an “=” sign before the division is performed. Don’t round the result of 0.0699/12 to 0.58 and enter 0.58 as i. Instead, enter =6.99%/12 or as a decimal =0.0699/12 for i.