If you borrow $500 from a credit union at 12% annual interest and $250 from a bank at 18% annual interest, what is the effective annual interest rate (that is, what single rate of interest on $750 would result in th same total amount of interest)?
Solution This solution is FREE courtesy of BrainMass!
Annual interest for one year at the rate 12% for $500 is given by,
I = Principal amount x number of years x rate/100
= 500*1*12/100 = 60 $
Now for an amount 250$ at the rate 18%, the interest amount is,
I2 = 250 * 1 * 18/100 = 45 $
Now the total interest we must pay is = 60 + 45 = 105 $
Thus in effct, w are paying $105 as interest for a total amount of (500 + 250 = $750)
Interest is 105$ for 750$ for one year.
Now what we need is what percentage of 750 is 105,
Rate of interest is R = I *100/(Principal * number of years) = 105*100/750 = 14
The answer is thus 14%