Question 350065: A book loaned out #250,000, part of it at the rate of 8% annual mortgage interest and the rest at the rate of 18% annual credit card interest. The interest received on both loans totaled $23,000. How much was loaned at each rate?
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! Amount of money lent out totals $250,000
x was loaned at 8% annual compounding assumed.
y was loaned at 18% annual compounding assumed.
Interest received on both loans totaled $23,000 for the year.
You have 2 formulas to work with.
x + y = 250,000 covers the amount of the loan.
.08*x + .18*y = 23,000 covers the interest earned for the year.
Solve both of these equations simultaneously and you will find how much was loaned out at each rate.
Use first equation to solve for y.
You get y = 250,000 - x
Substitute in second equation to get:
.08 * x + .18 * y = 23,000 becomes:
.08 * x + .18 * (250,000 - x) = 23,000
Simplify to get:
.08 * x + .18 * 250,000 - .18 * x = 23,000
Simplify further to get:
.08 * x + 45,000 - .18 * x = 23,000
Subtract 45,000 from both sides of the equation and combine like terms to get:
-.1 * x = -22,000
Divide both sides of the equation by -.1 to get:
x = 220,000
This means y = 30,000 because x + y = 250,000
The book loaned 220,000 at 8% and 30,000 at 18% to make a total interest of 17,600 + 5,400 = 23,000 for the year.
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