SOLUTION: 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.

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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