A bank loaned out $20,000, part of it at the rate of 9% annual interest, and the rest at 7% annual interest. The total interest earned for both loans was $1,480.00. How much was loaned at each rate?

Question

A bank loaned out $20,000, part of it at the rate of 9% annual interest, and the rest at 7% annual interest. The total interest earned for both loans was $1,480.00. How much was loaned at each rate?

what was owed at 9%

what was owed at 7%

Answer 1

Let a = the fraction of money invested at 9%

b = the fraction of money invested at 7%

Then 20,000a(.9) + 20,000b(.7) = 1480

and a + b = 1 Simplifying and multiplying the second equation by 1400

Then 1800a + 1400b = 1480

and 1400a + 1400b = 1400 Subtracting, we have

400a = 80 or a = .2 and b = .8

So, money invested at 9% = $4,000

money invested at 7% = $16,000 (assume 1 year loan at simple interest)