How do you calculate interest?

Question

Sherrie invested some money at 7% interest. Sherrie also invested $242 more than 4 times that amount at 6%. How much is invested at each rate if Sherrie receives $427.13 in interest after one year?

 

Answer 1

Let's assume Sherrie has invested $x at rate of 7% 

For this amount, Sherrie will earn interest amounting 7x/100 after one year,

The amount of other investment must have been, $(4x+242) and after 1 year at the rate of 6% interest this investment must earn $(4x+242)*(6/100)

hence, ( 7x/100)+ [(4x+242)*(6/100)]=427.13

=> 7x+(4x+242)*6= 42713 ........................................Multiplying both sides by 100

=>7x+24x+1452 = 42713 ........................................... Adjusting operators

=>31x+ =41261........................................................Subtracting 1452 from both the sides

=>x=1331 .................................................................Dividing both sides by 31

 

Trick is that at 7% interest means an investment of $100 earns in one year $7 or at 6% interest mean an investment  an investment of $100 earns in one year $6 

Hence for each dollar invested or for $1 investment at the rate of 7%, 7/100 dollars are earned in one year or  for $1 investment at the rate of 6%, 6/100 dollars are earned in one year

If $x in invested at the rate of 7% it earns x times more than an investment of $1 or if $(4x+242) invested at the rat e of 6% it earns (4x+242) times more than an investment of $1