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Working with Simple and Compound Interest

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%