Banking Word Problem

Question

A bank has loaned out $500,000, part of it at 6% per annum and the rest of it at 11% per annum. If the bank receives $43,750 in interest each year, how much was loaned at 6%?

Answer 1

Let the fraction f of $500,000 be loaned at 6% and the rest (1-f) be loaned at 11% pa. 

The total interest = 6/100*500000f + (1-f)*500000*11/100 = 30000f + 55000(1-f) = 55000 - 25000f = 43750

therefore 25000f = 11250 or f = 45/100 = 0.45. Therefore 500,000f = 225,000 was loaned at 6%