Rate word problem

Question

a bank loaned out $33,000 part of it at the rate of 5% annual interest, and the rest at 3% annual interest. The total interest earned for both loans was $1,380.00. How much was loaned at each rate?

Answer 1

Hi Brooke

 

Let's let X = amount loaned at 5%

Then 33000 - X = amount loaned at 3%

 

From the question, we know

.05X + .03(33000-X) = 1380

 

Distribute and rearrange terms

.05X + 990 - .03X = 1380

.02X + 990 = 1380

.02X = 390

X = 19,500

33000-X = 33000-19500 = 13500

 

So the bank loaned $19,500 at 5% and $13,500 at 3%. 

 

Hope this helps.