Maths tricks and shortcuts are the easiest and fastest ways in which you can solve mathematical problems in the upcoming Government exams. The quantitative aptitude or the numerical ability section are most commonly a part of all major tests and if a candidate can get shortcut tricks to solve this section quickly he or she may be able to score more overall in the examination.
1. Compound Interest
Given below are a few formulas that may save you some time during the exam while solving the compound interest problems:
(a) If compound interest is x% for 1st interval of time and is y% for the second interval of time, Then,
Net Effective Rate of Interest after the 2 intervals = x + y + (xy/100)
Note: This is applicable if both the time intervals are equal)
(b) If a sum of money, say P, amounts to A1 in a certain duration of time, say T, at Compound Interest and the same sum of money amounts to A2 in “2T” time at Compound Interest,
Then,
P/A1 = A1/A2
(c) If a sum of money, say P, amounts to A1 in a certain time duration, say T, at compound interest and the same sum of money amounts to A2 after T+1 years at compound interest
Then,
Rate of Interest = {(A2-A1) / A1} × 100
For example: Raj pays compound interest at 16% per annum to Shyam, which is compounded quarterly. What is the effective rate of interest per annum paid by Raj?
Solution:
Annual interest rate = 16%
So, the interest is paid quarterly, which makes a 4 time installment. Therefore, the rate of interest per quarter = 16/4 = 4%
Using (a) x + y + (xy/100).
4 + 4 + {(4×4)/100} = 8 + 0.16 = 8.16% for two quarters
For four quarters, 8.16% + 8.16% = 16.32%
2. Simple Interest
Take reference from the formulas given below and save some time while solving the questions in the final exam for the quantitative section:
(a) Difference between simple and compound interest for 2 years = {(PR)2/ (100)2}
(b) Difference between simple and compound interest for 3 years = {PR2 (300+R) / 1003}
For example: The difference between simple interest and compound interest for two years, on a certain sum of money at 4% per annum is Rs.800, when compounded annually. What is the sum of money on which the interest has been gained?
Solution:
Following (a) CI-SI = {(PR)2/ (100)2}
⇒800 = {(P×4)2/ (100)2}
⇒P = Rs. 707.11
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