Percentage , Simple Interest , Compound Interest 8 Flashcards
If an amount becomes N times in T years then -
It becomes N raised to 2 in 2T yrs
It becomes N raised to x in xT years
If T = 2 yrs then
SI - CI = P ( R/100 )sq
VAT
Value added tax
VAT =
Tax charged - tax paid
Recurring Deposit Account (R.D. Account) ?
A specific amount is determined by the depositor , which would be paid every month for a fixed period of time. At the end of the fixed time , a huge sum is given to the depositor (called Maturity value). The deposit is compounded quarterly at a fixed rate.
Computing total interest and total sum deposited in a recurring deposit
I = P x n(n+1)/2 x 12 x r/100
Total sum deposited = P x n
1/6 in %
16.66 %
1/7 in %
14.28 %
1/9 in %
11.11 %
1/11 in %
9.09 %
1/12 in %
8.33 %
1/13 in %
7.69 %
1/14 in %
7.14 %
1/15 in %
6.66%
1/17 in %
5.88 %
1/18 in %
5.55 %
1/23 in %
4.34 %
If a : b : : c : d ; then the fourth proportional to a,b,c is
d
Continued proportion
a : b : : c : d
If a : b : : b : c ; then c is the ……. to a and b
Third proportional
Compounded ratio of (a : b) , (c : d) , (e : f) is
(ace : bdf)
Duplicated ratio of (a : b) is
(a sq : b sq)
Triplicate ratio of (a : b)
(a³ : b³)
Sub triplicate ratio of (a : b)
(∛a : ∛b)
Componendo of a ratio a/b = c/d
(a +b)/ b = (c + d)/ d
Dividendo of a ratio a/b = c/d
(a - b)/ b = (c - d)/ d
What is the componendo-dividendo , if
a/b = c/d
(a+b) / (a-b) = (c+d) / (c-d)
Original value of a share
Nominal value
Ratio properties
Alterando - a/c = b/d
Invertendo - b/a = d/c
Componendo - (a+b)/b = (c+d)/d
Dividendo - (a-b)/b = (c-d)/d
Componendo et Dividendo -
(a+b)/(a-b) = (c+d)/(c-d)
Proofs of componendo and dividendo
a/b = c/d = k
a/b + 1 = c/d + 1
= (a+b)/b = (c+d)/d
a/b - 1 = c/d - 1
= (a-b)/b = (c-d)/d
Proof of componendo and dividendo
a/b = c/d = k
So a = bk and c = dk
(a+b)/(a-b) = (bk+b)/(bk-b)
= (k+1)/(k-1)
(c+d)/(c-d) = (dk+d)/(dk-d)
= (k+1)/(k-1)
1/19 in %
5.26%
1/21 in %
4.76
1/22 in %
4.54%
1/23 in %
4.34%
1/24 in %
4.16%
Slump means
No of sales
1/12 in %
8.33%
For a rectangles : If length is increased by a% and breadth by b% , what is the percentage change in area
{a ± b ± (a x b)/100}%
+ve for increase and vice versa
In a ratio first term is called …… while second term is called …….
Antecedent , Consequent
Alligation
Rule that enables us to find the ratio in which 2 or more quantities at the given price be mixed to produce a mixture of a desired price.
Mean price
Cost of a unit quantity of mixture is called the mean price.
Rule of Alligation :
If 2 ingredients are mixed :
Qty of cheaper/Qty of dearer =
C.P of dear - M.P/ M.P - S.P of cheap
M.P stands for : mean price of that mixture.
Money invested in business
Capital
Active partner or working partner
Partner who manages the business
Sleeping partner
Partner who just invests money
B is k times efficient than A means
If A takes x days to complete a task , then b takes x/k days to do it
A certain distance is covered from A to B at u km/hr and the same distance from B to A in v km/hr. Then avg speed is equal to
2uv/u+v (not important)
Time taken by train of a meters to pass a pole or a standing man :
Time taken to cover a metres
a - speed down streams
b - speed down streams
Then rate of stream
1/2(a-b) km/hr
a - speed down streams
b - speed down streams
Then speed of boat in still waters
1/2 (a+b)
Time period vs Conversion period
Time period- period for which sum is borrowed
Conversion period - period of time at the end in which the interest is calculated
If interest is compounded annually and time is a fraction then compound interest is
A = P (1 + R/100)² (1 + (R/4)/100
