*Simple Interest Tips, Tricks, and Results*

*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}

R^{2} = 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**

**Simple Interest Tips, Tricks and Results**

**The rate of interest for t**_{1}years is r_{1}% , t_{2}years is r_{1}%, t_{2 }years is r_{3}%.If a man gets interest of Rs x**for (t**_{1}+ t_{2}+ t_{3}=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*

*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*

*Simple Interest Tips, Tricks, and Results*

**Change in Simple Interest when time changes from T**_{1 }to T_{2}is given by the formula:

**Change in Simple Interest when principal changes from P**_{1 }to P_{2}is given by the formula:

**Change in Simple Interest When rate of interest changes from r**_{1}to r_{2}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 P_{1}to P_{2}

*Simple Interest Tips, Tricks, and Results*

*Simple Interest Tips, Tricks, and Results*

**If a person deposits A _{1} amount at r_{1}% per annum and amount A_{2 }at r_{2}% per annum, then the rate of interest for the whole sum is {(A_{1}r_{1} + A_{2}r_{2})/(A_{1}+A_{2})}**

**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 {(A_{1}r_{1} + A_{2}r_{2})/(A_{1}+A_{2})} , the rate of interest is

[{(1000 x 4) + (2000 x 5)}/(1000 + 2000)]
= 14000/3000

14/3%

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**A certain amount is invested for certain time but at different rates. When rate per annum is r**_{1} the amount becomes x_{1} but at rate r_{2 }per annum, the amount becomes x_{2} . Time, t, is given by the formula:

t = {(x_{1} – x_{2})/(x_{2}r_{1} – x_{1}r_{2})}*100

_{1}the amount becomes x

_{1}but at rate r

_{2 }per annum, the amount becomes x

_{2}. Time, t, is given by the formula: