Interest rate word problem: "Justin borrowed a total of $6000 from two student loans..."

[Kapo8701]

Justin borrowed a total of $6000 from two student loans. One loan charged 2% simple interest and the other charged 1.5% simple interest, both payable after graduation. If the interest he owed after 5 years was $462.50 , determine the amount of principal for each loan.

I kind of hate word problems not my strong point,

 

[stapel]

Justin borrowed a total of $6000 from two student loans. One loan charged 2% simple interest and the other charged 1.5% simple interest, both payable after graduation. If the interest he owed after 5 years was $462.50 , determine the amount of principal for each loan.

I kind of hate word problems not my strong point,

Well, "practice makes perfect", so let's see what you've tried so far. We'll then be able to try to help you move forward.

For instance, you started by picking a variable (what variable?) to stand for something (stand for what?), and... then what?

Please be complete. Thank you!

 

[Kapo8701]

I'm not sure where to start

 

[Bruce]

X+Y=6000 so Y=6000-X

that means borrow X dollar at first loaner and (6000-X) dollar at second loaner

Put loan amounts in simple interest formula (5 yr each)

 

[Steven G]

I have serious problems with this problem. It says after 5 years he owed $462.50 in interest--did he pay any interest before the 5 years???
Haven't said that the OP should just assume that there was no interest paid before the five year period.

To Kapo, if Justin borrowed $1200 at 2% simple interest, then how much interest does he owe after 5 years? How about if he borrowed $2200 at 2%?

Just do the same with these unfriendly amounts that Bruce spoke about. How much should the interest from 2% plus the interest from 1.5% be after 5 years? Hint, this amount was outright given.

 

[khansaheb]

Justin borrowed a total of $6000 from two student loans. One loan charged 2% simple interest and the other charged 1.5% simple interest, both payable after graduation. If the interest he owed after 5 years was $462.50 , determine the amount of principal for each loan.

I kind of hate word problems not my strong point,

continuing from response #4 (@Bruce)

How much total interest will be accrued by first loan = I₁

How much total interest will be accrued by second loan = I₂

Given:

I₁ + I₂ = ?

Two equations and two unknowns ................... Solve for X and Y

 

[Bruce]

simple interest formula: I = p*r*t

I is the interest amount
p is the loan amount
r is the interest rate
t is the number of years

example, borrow $4,000 for 3 yr @ 9.5% interest rate:

9.5% = 9.5/100 = 0.095
I = (4000)(0.095)(3) = 1140
so interest at end of 3 yr is $1,140

example, unknown loan amount:
I = (X)(0.095)(3) = 0.285X
so interest at end of 3 yr is 0.285X dollar

 

[Bruce]

did he pay any interest before the 5 years?

I don't think so. They would give payment info when loan has many payments.

 

[Steven G]

I don't think so. They would give payment info when loan has many payments.

Are you sure about that? I am sure that the author of the problem meant just what you are thinking but should have stated it!

 

[Dr.Peterson]

Are you sure about that? I am sure that the author of the problem meant just what you are thinking but should have stated it!

But isn't that exactly what this means?

One loan charged 2% simple interest and the other charged 1.5% simple interest, both payable after graduation.

It seems clear to me that the answer to your question,

It says after 5 years he owed $462.50 in interest--did he pay any interest before the 5 years???

is no.

"Simple" means there's only one payment, and "payable" means that this is when he owed it, so that we have to assume that he was in a 5-year program.

Sometimes we can quibble over wording, and often problems are unrealistic, but such quibbles don't help students gain confidence. (After the problem has been solved, it can be worth pointing out that in the real world, you would have wanted to ask a couple questions to confirm your interpretation. But this is not the real world.)

 

[stapel]

"Simple" means there's only one payment...

No, "simple interest" means that the interest is not compounded.

...let's see what you've tried so far.... For instance, you started by picking a variable (what variable?) to stand for something (stand for what?), and... then what?

I'm not sure where to start

Oh, so they haven't covered this material in class yet, or you missed that day in class? Unfortunately, we cannot here reasonably attempt to replace that missing instruction. Fortunately, there are loads of lessons available online, such as in (this listing).

Please read *at least two* lessons from the listing (after which the hints and suggestions you've been given, such as where the start, should make more sense to you). Then please attempt the exercise. If you get stuck, you can then reply with a clear listing of your efforts so far.

Thank you!

 

[Bruce]

Are you sure about that?

Yes, very sure. If I judge wording, I think 1.5% and 2.0% interest for student loan is what not make sense!