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Simple Interest

Simple Interest | Tips & Tricks

Simple Interest Tips, Tricks, and Results

  • If the interest on a sum of money is 1/x  of the principal, and the number of years is equal to the rate of interest then rate can be calculated using the formula: √(100/x)

Derivation for this result:
We Know SI = {(P x R x T)/100}
Put SI = P/x  ; and T=R
P/x = {(P x R x T)/100}
R2 = 100/x
R = √(100/x)

Example : The interest on a sum of money is 1/16 of the principal, and the number of years is equal to the rate of interest. What is the rate percent?

Solution :

Using the above concept :

R = √(100/x)

R = √(100/16)

R = 5/2%

Simple Interest Tips, Tricks and Results

  • The rate of interest for t1 years is r1% , t2 years is r1%, tyears is r3 %.If a man gets interest of Rs x for (t1+ t2 + t3 =n)  years, then principal is given by

Example: The rate of interest for 3 years is 4%, 5years is 6%,1 years is 5%. If a man gets interest of Rs. 4700 for 9 years, calculate the principal amount?

Example: A sum of money becomes 4 times in 20 years. Calculate the rate of interest.

Example: A sum of money becomes 4 times in 20 years. Calculate the rate of interest.

Solution:

Using the above result:

R = [{100(x-1)}/n]%

R = [{100(4-1)}/20]=15%

Simple Interest Tips, Tricks, and Results

If a sum of money becomes x times in n years at simple rate of interest, then the time is calculated as

n= {100(x-1)/R}

Example:A sum was put at SI at a certain rate for 3 years. If the sum would have put at a 2% higher rate, it would have yieldedRs 900 more. What will be the principal?

Solution:

Use the above formula:

P= {100X/(nX r)}

P= {(900 x 100)/(3 x2)} = Rs. 15000

This tooltip is a reverse of the last one. A sum is put at SI at a certain rate for n years. If the sum would have put at a r% lower rate, it could yield Rs X less. So the principal will be:

P= {100X/(n * r)}

Example: A sum was put at SI at a certain rate for 3 years. If the sum would have put at a 2% lower rate, it could yield Rs 900 less. What will be the principal?

Solution:

Using the formula, we arrive at the following:

P= {100X/(n * r)}

P= {(900*100)/(3*2)}

P = Rs. 15000

Simple Interest Tips, Tricks, and Results

  • Change in Simple Interest when time changes from Tto T2 is given by the formula:

  • Change in Simple Interest when principal changes from Pto P2  is given by the formula:

  • Change in Simple Interest When rate of interest changes from r1to r2 is given by the formula:

Example: Simple interest on Rs 200 increases by Rs 50 when time increases by 5 years. Find rate percent per annum.

Example: If the SI on Rs 1000 be more than the interest on 2000 by Rs 20 in 4 years, find the rate per annum.

Solution: When principal changes from  P1to P2

Simple Interest Tips, Tricks, and Results

If a person deposits A1  amount at r1% per annum and amount Aat r2% per annum, then the rate of interest for the whole sum is {(A1r1 + A2r2)/(A1+A2)}

Example: A man deposits Rs.1000 at 4% per annum and Rs 2000 at 5% per annum, find the rate of interest for the whole sum.

Solution: 
Method-1:
Using the formula for, Simple Interest (SI) =  {(P x R x T)/100}
X = {(1000 x 4 x 1)/100} = 40
Y = (2000 x 5 x 1)/100 = 100
Total interest = 100+40=Rs. 140
Total principal =1000+2000=Rs.3000
Using the formula:
140 = {(3000 x R x 1)/100}
R = 14/3%

Method-2:
Applying above concept {(A1r1 + A2r2)/(A1+A2)} , the rate of interest is
[{(1000 x 4) + (2000 x 5)}/(1000 + 2000)] = 14000/3000
14/3%

A certain amount is invested for certain time but at different rates. When rate per annum is r1 the amount becomes x1 but at rate  rper annum, the amount becomes x2 . Time, t, is given by the formula:
t = {(x1 – x2)/(x2r1 – x1r2)}*100

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