Question 1112210: A man lends a sum of money to his local council and receives $63 interest on the loan
Each year. When the rate of interest rises by 0.5%, the annual interest raised to $67.50.
Calvulate the sum of money lent to the council and the new percentage of interest.
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! let x = the amount of money he lends to the council.
let r be the interest rate of the loan.
the interest on the loan is 63 per year.
x * r = 63
when the interest rate on the loan is increased by .5%, the annual interest is raised to 67.50.
.5% / 100 is equal to .005.
x * (r + .005) = 67.5
you have 2 equations that need to be solved simultaneously.
they are:
x * r = 63
x * (r + .005) = 67.5
simplify the second equation and leave the first equation as is to get:
x * r = 63
x * r + .005 * x = 67.5
since x * r = 63 from the first equation, replace x * r in the second equation by 63 to get:
second equation becomes:
63 + .005 * x = 67.5
subtract 63 from both sides of this equation to get:
.005 * x = 4.5
divide both sides of this equation by .005 to get:
x = 4.5 / .005
this results in x = 900.
go back to your original equation and replace x with 900 and solve for r.
the first original equation is:
x * r = 63
replace x with 900 to get:
900 * r = 63
solve for r to get:
r = 63/900 = .07
in the second original equation, replace r + .005 with .075
the first and second original equations now become:
900 * .07 = 63 becomes 63 = 63, which is true.
900 * .075 = 67.5 becomes 67.5 = 67.5, which is true.
both original equations are true when r = .07.
this confirms the solution is correct, given the original equations are correct.
interest rate percent is 100 * interest rate.
conversely, interest rate is interest rate percent / 100.
you had to work with interest rate, not percent.
that'w why we used .5%/100 = .005, rather than .5%, in the equations.
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