Banking

[mathxyz]

A bank loaned out $12,000, part of it at the rate of 8% per year and the rest at the rate of 18% per year. If the interest received totaled $1000, how much was the loaned at 8%?

Can I use the famous formula I = prt where I = interest, p = principal and r = rate? If so, can someone help me set up the right equation that will guide me to the correct answer?

 

[tkhunny]

A bank loaned out $12,000, part of it at the rate of 8% per year and the rest at the rate of 18% per year. If the interest received totaled $1000, how much was the loaned at 8%?

Can I use the famous formula I = prt where I = interest, p = principal and r = rate?

Good call. You are on the right track.

Unfortunately, there is one important thing missing from this problem, the time period. Was it paid back over exactly one year? It will be easier if it is, but it doesn't say that.

Generally, start by naming things.

X = Amount at 8%

After saying that, it is not hard to notice that 12000-X = Amount at 18%
Without first saying that (X = Amount at 8%), it is very hard to solve this problem or understand what it is we are talking about. That upfront, clear, and precise definition statement is very important. It is ALWAYS a good place to start, no matter the problem statement.

 

[mathxyz]

Now...

Are you saying that "12000-X = Amount at 18%" is all I need to solve this question? I can go as far as x = "what I am looking for," but that's as far as I can go with most complicated word problems. See my point? If the bank loaned $12,000, it should have been clear to me that to GIVE AWAY means to subtract but when I first read the question, I was NOT able to picture your equation. Your reply?

 

[Denis]

Re: Now...

Are you saying that "12000-X = Amount at 18%" is all I need to solve this question? I can go as far as x = "what I am looking for," but that's as far as I can go with most complicated word problems. See my point? If the bank loaned $12,000, it should have been clear to me that to GIVE AWAY means to subtract but when I first read the question, I was NOT able to picture your equation. Your reply?

A certain amount is at 8%: let that amount = x;
then 12000-x is what remains, and the rate on that is 18%:
that's what TK is telling you; do you understand that?

(assuming this is a 1 year arrangement)
The interest will be 8% on x and 18% on 12000-x;
and since the interest is 1000, then:
.08x + .18(12000 - x) = 1000

Now solve for x

 

[mathxyz]

ok

I can now solve for x.