One of the topics commonly tested in the GMAT Quant section is that of Simple Interest. While the formulas and concepts applied herein are simple enough, a lot of test takers get caught up in the terminology surrounding the concepts and therefore get their answers on this topic wrong. Here, then, are the concepts on Simple Interest that you can get tested on when you take the GMAT, including the terminology:
Simple Interest = P x R x T/100
Where P: Principal (or the amount originally lent out)
R: Rate of interest (expressed in terms of %)
T: Time period for which the loan is made
Common mistakes made by test takers when dealing with Simple Interest problems
1. Taking the rate of interest in decimals, instead of in percentage terms: Remember, the 100 in the denominator of the formula is there because it assumes that the rate of interest (R) will be taken in percentage terms, not in decimals.
Example: If P = $1000, R = 4% per annum, and T = 3 years,
SI = 1000 x 4 x 3 / 100 = 120
Do NOT take SI = 1000 x 0.04 x 3 / 100 = 1.2
2. Interpreting SI to mean the amount to be paid back: The SI formula calculates just the interest to be paid back at the end of the loan period. It does NOT include the amount.
Example: If $1000 is loaned for 3 years at 4% annual rate of interest, the amount to be paid back at the end of the 3 years = 1000 x 3 x 4 /100 + 1000 = 1120
Remember to add the principal when calculating the amount due.
3. Adjusting both the time and the rate of interest when dealing with periods of loan that are not full years: Remember, if the calculation is to be made on a semi-annual basis, then adjust either the time period or the rate of interest, not both.
Example: If $1000 is loaned for 6 months at 4% annual rate of interest then
SI = 1000 x 4 x (6/12)/100 = 20 [Dividing the time period by 12 to convert it into half an year or 6 months]
OR
SI = 1000 x (4/2) x 6 /100 = 20 [Dividing the annual rate of interest by 2 to convert it into a monthly rate of interest]
DO NOT make the mistake of using the formula as:
SI = 1000 x (4/2) x (6/12) / 100 = 10 [Here the rate of interest has been converted to a monthly rate but the time period has been converted from months (6) to years (6/12), which IS WRONG]
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