Simple Interest solved Problems with tricks

SIMPLE INTEREST 

1. A sum of Rs.550 was taken a loan. This is to be repaid in two equal annual instalments. If the rate of interest be 20% compounded annually, then the value of each instalment is :

Answer: Rs. 360
Explanation:
Let the value of each instalment be Rs.x.
[ x / ( 1 + ( 20 / 100 ) ) ] + [ x / ( 1 + ( 20 / 100 ) )2 ] = 550
( 5x / 6 ) +( 25x / 36 ) = 550
x = Rs. 360


2. If the simple interest on Rs. 1120 for 2 years is Rs.8000/-, what is the rate of interest percent per annum?

Answer: 7%
Explanation:
Interest = Rs. 1120
Time = 2 years
Principle = Rs. 8000
Simple interest = [ ( Principle * Time * Rate ) / 100 ]
Rate = ( Simple interest * 100 ) / ( P * T )
Rate = ( 1120 * 100 ) / ( 8000 * 2 )
Rate = 56 / 8
= 7%


3. The simple interest on Rs. 1820 from March 9, 2003 to May 21, 2003 at [ 7 * ( 1 / 2 ) ]% rate?

Answer: Rs. 27.3
Explanation:
Time = ( 22 + 30 + 21 ) days
= 73 days
Rate = [ 7 * ( 1 / 2 ) ]%
= ( 15 / 2 )%
= ( 1 / 5 ) years ( ∴ 73 / 365 = 1 / 5 )
Simple Interest = ( principal * rate * time ) / 100
= [ 1820 * ( 15 / 2 ) * ( 1 / 5 ) ] / 100
= ( 1820 * 15 * 1 ) / ( 2 * 5 * 100 )
= 273 / 10
= Rs. 27.3


4. The difference between the interests received from two different banks on Rs. 500 for 2 years, is Rs. 2.50. Find the difference between their rates?

Answer: 0.25
Explanation:
Let the rates be x% and y%.
⇒ [ ( 500 * x * 2 ) / 100 ] - [ ( 500 * y * 2 ) / 100 ) ] = 2.5
⇒ ( 1000x / 100 ) - ( 1000y / 100 ) = 2.5
⇒ 10x - 10y = 2.5
⇒ 10 ( x - y ) = 2.5
x - y = 2.5 / 10
x - y = 0.25


5. A certain sum of money at simple interest amounts to Rs.1260 in 2 years and to Rs.1350 in 5 years. Find the rate percent per annum?

Answer: 2.5%
Explanation:
Simple Interest for 3 years = Rs.( 1350 - 1260 ) / 3
= Rs. 90 /3
= Rs. 30 Simple Interest for 2 years = Rs.[ ( 30 ) * 2 ]
= Rs. 60
Sum = Rs.( 1260 - 60 )
= Rs. 1200
Rate = ( 100 * 60 ) / ( 1200 * 2 )
= 5 / 2
= 2.5%


6. How much time will it take for an amount of Rs. 900 to yield Rs. 81 as interest at 4.5% per annum of simple interest?

Answer: 2 years
Explanation:
Principal = Rs. 900
Simple Interest = Rs. 81
Rate = 4.5 %
Time = ( 100 * Simple Interest ) / ( Principal * Rate )
= ( 100 * 81 ) / ( 900 * 4.5 )
= 8100 / 4050
= 2 years


7. A sum of money at simple interest amounts to Rs. 815 in 3 years and to Rs. 854 in 4 years. Find the sum?

Answer: Rs. 698
Explanation:
Simple Interest for 1 year = Rs. ( 854 - 815 )
= Rs. 39
Simple Interest for 3 years = Rs. ( 39 * 3 )
= Rs. 117
Principal = Rs. ( 815 - 117 )
= Rs. 698


8. A sum fetched a total simple interest of Rs. 4016.25 at the rate of 9 percent per annum in 5 years. What is the sum?

Answer: Rs. 8925
Explanation:
Principal = ( 100 * Simple Interest ) / ( Rate * Time)
= Rs. [ ( 100 * 4016.25 ) / ( 9 * 5 ) ]
= Rs. ( 401625 / 45 )
= Rs. 8925


9. How much time will it take for an amount of Rs. 450 to yield Rs. 81 as interest at 4.5% per annum of simple interest?

Answer: 4 years
Explanation:
Time = ( 100 * Simple Interest ) / ( Principal * Rate )
= ( 100 * 81 ) / ( 450 * 4.5 ) years
= 4 years


10. A sum of Rs. 800 amount to Rs. 920 in 3 years at simple interest. If the interest rate is increased by 3%, it would amount to how much?

Answer: Rs. 992
Explanation:
Simple Interest = Rs. ( 920 - 800 ) = Rs. 120
Principal = Rs. 800
Time = 3 years
Rate = ( 100 * Simple Interest ) / ( Principal * Time )
= [ ( 100 * 120 ) / ( 800 * 3 ) ] %
= 5%
New Rate = ( 5 + 3 ) %
= 8 %
New simple Interest = ( Principal * Rate * Time ) / 100
= Rs. [ ( 800 * 8 * 3 ) / 100 ]
= Rs. ( 8 * 8 * 3 )
= Rs. 192
New amount = Rs. ( 800 + 192 )
= Rs. 992