Word problem

Question

Grace is able to obtain two loans to purchase a house. She borrows $60,000 from a bank and $96,000 from a savings and loan company whose lending rate is 1% more than the bank's. Determine the interest rate for each loan if her total monthly interest charge on the loan is $600.

Answer 1

1% charge on the $96,000 would be $960 > $600

so the bank must "charge" a negative interest to get the combined interest charge = $600

60x + 96(x+1) = 0.6

156x = 0.6 -0.96 = -0.36

x = -0.36/156 = about - 0.00231 = -0.231% on the bank loan

and x+1 = 0.769% on the S&L loan

60(-0.00231) + 96(0.00769) = -0.138 + 0.738 = 0.6

The bank :charges negative interest on $60,000 and

S&L charges less than 1% on the $96,000 loan

-0.231% and +0.769%