A bank loaned out $30,000 part of it at the rate of 6% annual interest, and the rest at 9% annual interest. The total interest earned for both loans was $2,280.00. How much was loaned at each rate?

Answer 1

Let a = the fraction of money invested at 6%

Let b = the fraction of money invested at 9%

S1 = total money at 6% at end of period

S2 = total money at 9% at end of period

S1 + S2 = 30,000 + 2280 = 32280

a + b = 1

S1 = a(30000)(1.06) = 31800a

S2 = b(30000)(1.09) = 32700b adding S1 and S2 we get

S1 + S2 = 32280 = 31800a + 32700b and

1 = a + b

Solving for a & b we get a = .466666 & b = .533333

30000a = 14000 (Invested at 6%) and 30000b = 16000 (Invested at 9%)