Question 350065
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.