# Principles of Quantitative Methods

2011

Table of Contents

Question 1 – Difference between Simple Interest and Compound Interest3 1.0 Simple Interest3

1.1Compound Interest4

Question 2 – Difference between Depreciation by Straight Line Method and Depreciation by Reducing Balance Method6 2.0 The Difference6

Question 3 - Standard Deviation and Quartile Deviation7

Standard Deviation7

Quartile Deviation8

3.0 Purpose of Calculating Standard Deviation and Quartile Deviation8 3.1 Calculation of Standard Deviation and Quartile Deviation8 Reference9

Question 1 – Difference between Simple Interest and Compound Interest To know the difference between simple and compound interest, one must have an overview of the interest concept and the rationale behind interest being paid to the lender of the funds. The concept of interest is that it is the cost of borrowing money (Salkind, 1998). The lender of the funds is foregoing the utility of using the funds at the present amount of time, and is also foregoing the opportunity to use these funds at the present moment. For this purpose, a cost is associated with the lending of the funds which is termed as interest (Henry, 1990). This concept is important for it helps to understand the difference between the concept of simple interest and compound interest, as well as their calculations. 1.0 Simple Interest

Simple interest is the cost which is levied on the original amount only. The initial fund which is lent to the borrower is termed as principal (Lewin, 1981). The concept of simple interest is that the fixed charge is levied on the borrower of the funds which is proportional to the amount of time for which money is lent. It is calculated on the principal only. Accumulated interest from prior periods is not used in calculations for the following periods (Lohr, 1999). For example, if the lender of the funds decide that his/her opportunity cost for foregoing the use of the funds is ten percent, and the person lends a thousand dollars; then according to the concept of simple interest the person will be entitled to only a hundred dollars for the year, for the next year and for any year subsequent to that. The formula for the calculation of simple interest is given by: Simple Interest = Principal x Interest Rate per Year x Time in Years In books of economics and statistics, this formula is also give by: Simple Interest = p * i * n

Where – p = principal (original amount borrowed or loaned), i = interest rate for one period, and n = number of periods It should be noted that simple interest in general applications is used for a single period of less than a year, such as 30 or 60 days. This is because simple interest calculations are biased against the lender of the funds when the time period for the lending of the funds is long (Henry, 1990). When the funds are lent for more than a year, the borrower is not only borrowing the principal, but he is also getting the benefit of using the income which is produced by these funds as a source of capital as well. Given below are two calculations to exhibit the usage of the formula for simple interest. The first instance shows the calculation for three years, and the second example shows how to calculate simple interest for a period of mere three months. Example 1: Lender gives $5,000 for 3 years at 7% simple annual interest. Simple Interest = p * i * n = 5,000 * 0.07 * 3 = $ 1,050

Example 2: Lender gives $5,000 for 90 days at 7% simple interest per year (assume a 365 day year). Simple Interest = p * i * n = 5,000 * 0.07 * (90/365) = $ 86.30 Note: There is a linear relationship between the amounts and the time period. If the interest for one year is a thousand dollars, then for three years it is going to be three thousand dollars 1.1Compound Interest

Compound interest is the one which is calculated based on the original principal which was lent as well as on every subsequent interest payments (Salkind, 1998). For example, when...

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