# SIMPLE INTEREST FORMULAS-QUESTIONS SOLUTIONS WITH EXAMPLES-FULL SET OF ALL FORMULAS

Simple interest questions are very important questions and asked in all types of exams whether it is competitive exams or entrance exams or qualifying exams. From lower class to higher degree classes, simple interest problems are more important for every person to know. However, not every person is familiar with all formulas of simple interest. So I decided to put on all types of shortcut formulas of simple interest.
Before remembering shortcut formulas, let me explain some basic terms of simple interest.
·         What is interest?
If a person borrows some money from a lender, he/she pays a certain amount extra for the use of that money. That money is called interest. It is of two types:

1.       Simple interest
2.       Compound interest
·         Principal: Principal is the amount of loan borrowed.
·         Amount: it is the sum of Principal and Interest.
Compound interest- all formulas-are soon to come in the next post
So here is a full set of all shortcut formulas of simple interest:

First understand these shortcut terms
A= amount
P= Principal
SI= Simple Interest
R= rate
T= time
Formulas:
·         A= P+ SI

·         SI= (P*R*T)/100

·         P=100*SI/RT

·         R= 100*SI/PT

·         T= 100*SI/PR

·         A= P{1+(RT/100)}

·         When time is given in months(M), convert it into year by dividing it with 12
SI= PRM/1200

·         When time is given in days(D),  convert it into year by dividing it with 365
SI= PRD/36500

·         A sum of money becomes n times in t years at simple interest, then rate of interest will be
R= 100(n-1)/T    %

·         A sum of money becomes n times at R% per annum at simple interest, then
Time= 100(n-1)/R             years

·         If any sum is n times of simple interest, then
T= 100n/R            years
R= 100n/T            %

·         A person invests a certain amount of money at some rate of simple interest. If he had invested it at R% higher, then that person would have earned x (money- rupees or any currency of world) more. The sum that person invested  = 100x/nR

·         If at some rate of simple interest, any sum becomes n1 times in T1 years, then the sum becomes n2 times in
T2= T1(n2-1)/(n1-1)        years

·         If at the rate of R1 % of simple interest, any sum becomes n1 times in a certain amount of time, then then in the same time, the sum becomes n2 times if
R2= R1(n2-1)/(n1-1)        years

·         A person (A) lends x money to B for T1 years and y money to C for T2 years. The person Q money all together as interest, then the rate of interest was
= 100Q/(P1T1+P2T2)

Example: 1
A sum of money gets doubled at 12% per annum. Then find the time?
solution:
time= 100(n-1)/R
=100(2-1)/12
=100/12
= 25/3 years

Example:2
a person borrows  x \$ say \$ 5000 for t years say 2 years at r1% say 4% per annum on simple interest. He uses his smartness and lends it to another person at bigger rate r2 % say 6.25% per annum for the same time. then his total gain in this transaction will be

={PT(r2-r1)}/100
= {5000*2(6.25-4)}/100
= 100*2.25
=  \$ 225