# Simple Interest and Compound Interest Practice problems with shortcut tricks

Example 1: A sum of Rs 12,000 at simple interest amounts to Rs. 15,000 in3 years Find rate %.

SI=15000-12000=3000Rs.

SI= P*r*t/100

Rate= 3000*100/12000*3

=8.3%

Example 2: what annual payment will discharge at a debt of Rs 750 due in 5 years, the rate of interest given is 5% per annum?

Direct Formula

**Annual payment= 100A/[100t+rt(t-1)/2]**

=100*700/[100*5+5*5(5-1)/2]

=700*100/550

=127.27

Example 3: A certain sum of money amounts to Rs. 756 in 2 years and to Rs. 873in 3^{1}/2 years. Find the sum and the rate of interest?

SI FOR 1.5 year= 873-756=Rs117

So SI for 2 years = 117*2/1.5= Rs156

P=756-165=Rs600

Now by using simple formula we can get

Rate= 100*156/600*2

=13% per annum

Example 4: Find the SI on Rs 14600 at 8 ¼% per annum for period from 10 March 2015 to 17^{th} June 2015.

Here r=33/4% Per annum

t=Number of days in March, April, May, June

t=21+30+31+17=99days

SI= 14600*33/4*99/365*1/100

=Rs 326.70

Example 5: Aman lent a certain sum of money at 16% per annum simple interest for period of 8 years. Interest alone he got Rs 336 then what money he lent?

Let the amount lent is X

Then SI= P*r*t/100

X*8*16/100=x + 336

28x= 33600

X=Rs12000

Example 6: A sum of money double itself in 10 years at simple interest the find rate of interest?

Let the sum be 100. After 10 years it becomes 200. So interest = 200-100=100

So by just putting values in simple formula

Rate of interest= 100*100/100*10=10%

Direct Formula=

**Time x rate=100(multiple number of principal-1)**

Rate=100(2-1)/10=10%

Example 7: A sum was put at Simple interest at a certain rate for 2 years. Had it been put at 3% higher rate, then it would have fetched 1200 more. Find sum

Let the sum be Rs x and original rate is y% per annum. The new rate= (y+3)%

So x.(y+3).2/100 –x.y.2/100=1200

=10000

**Direct Formula= More interest x 100/time x more rate**

=1200×100/2×6

=10000

Example 8: A sum of Rs 3120 lent out in two parts n such a way that interest on one part at 10% for 5 years is equal to that on another part at 9% for 6 years. Find the two sums?

Each interest= 1^{st} part*5*10/100=2^{nd} part*6*9/100

1^{st} part/2ndpart= 6*9/5*10= 27/25

1^{ST} PART= 3120*27/27+25= Rs 1620

2^{nd} part= 3120-1620=Rs 1500

Example 9 . Reena invested an amount of Rs 9000 at 15 % per annum compound interest for 2 years. How much interest she would get?

When interest is compounded annually,

Amount = P(1+r/100)^{t}

Amount=9000(1+15/100)^{3}

=Rs 11902.5

Interest= 11902.5-9000= Rs2902.50

Example 10. Shyam borrowed Rs 24000 from two banks at 10% simple interest basis and another bank at 10 % compound interest basis for 3 year. How much interest he Had paid more to second bank ?

Simple Interest for one bank= 24000*10*3/100

=Rs 7200

Now compound Interest from another bank=

24000(1+10/100)^{3} -24000

=RS 7944

Difference= Rs7944-Rs7200

=Rs.744

Example 11: At what rate amount 80,000 will become Rs 88,200 if compounded yearly for 2 years?

So 80,000(1+r/100)^{2}=88,200

(1+r/100)^{2}= 88,200/80,000

(1+r/100)^{2}=441/400=> (21/20)^{2}

(1+r/100)=21/20

R=5%

Example 12. A certain sum of money amounted to Rs 575 at 55 in a time which Rs 750 amounted to Rs 840 at 4%. If the rate of interest is simple, then find sum?

Interest= Rs 840-Rs750= Rs90

Time= 90*100/750*4

=3 year

Now

**Sum= 100*Amount/(100+rt)**

Sum= 100*575/100+3*5

=Rs500

Example 13: A sum of money at compound interest amounts to thrice itself in 3 years. In how many years will it be 9 times?

Suppose the sum= Rs x then

3x=x(1+r/100)^{3}

3=(1+r/100)^{3}

Squaring on both side

9=(1+r/100)^{6}

Multiplying both side by X

9x=x(1+r/100)^{6}

The sum will be 9 times in 6 year

**Difference between Compound Interest & Simple interest Concept For Two years **

CI – SI =sum(r/100)^{2}

For Three Year

**CI – SI = sum(r/100) ^{2}*(300+r)/100**

For Two year

**CI/SI=(200+r)/200**

Example 14. Find the difference between compound interest and simple interest for the sum of Rs 1000 at 10% per annum for 2 years.

Difference= sum(r/100)^{2}

Diff= 1000(10/100)^{2}

=Rs 10

Example 15. Find the difference between compound interest and simple interest for the sum of Rs 8000 at 2.5% per annum for 3 years.

Difference= sum(r/100)^{2}*(300+r)/100

=8000 * 2.5^{2 }*(300+2.5)/ 100^{3}

=Rs 15.12