If you borrow 450 from a credit union at 9 annual interest a

If you borrow $450 from a credit union at 9% annual interest and $200 from a bank at 12% annual interest, what is the effective annual interest rate (that is, what single rate of interest on $650 would result in the same total amount of interest)? (Round your answer to one decimal place.)

Solution

for credit union

Pc = credit from credit union = $450, Rc= rate by credit union =9%

Ic = Annual interest for credit union = 450 * 9 *1/100 = 450* 0.09 = $40.5

for bank

Pb =$200, Rb =12%

Ib = Annual interest for bank = 200 *12*1/100 = $24

total interest I = Ic + Ib = $40.5 + $24 = $64.5

total principle ammount P =Pc + Pb =450+ 200 = $650

let R be the effective interest rate

then I = P *R *1/100

R = (I *100)/P

=(64.5 *100)/650

= 9.92307692308 %   is the answer