After earning interest, the balance of an account is $420. The new balance is 7/6 of the original balance. How much interest did it earn?

Question

This is a question i worked on for quite a moment that i need some help on.  I hope this isnt to much of a hard on for you  thankyou.

Answer 1

Hmm.  I think there are two answers to this question.  Probably this is the one you don't want:

 

7/6 = 1.1667  Since the new amount is 1.1667 times larger, the account earned 16.67%

 

The one you probably want goes more like this: 

 

One intuition is that if you divide $420 up into 7 chunks, 6 of them are the original balance (6/6) and one is new (1/6).  So divide $420 by 7, and there's your answer.

 

If that doesn't compute, we have this:

Let M be the original balance.  Then the interest is $420 - M.  If I is the interest, then

I = $420 - M

 

Now, we were told that the new balance is (7/6) M.  So that means

(7/6) M = $420.

 

We'll just multiply both sides by (6/7):

 

1 M = (6/7) $420 = 6 ($420 / 7). 

M = 6 ($420 / 7)

 

I'll let you finish that bit off, ok?  I think you can solve for M from here.

 

Ok, now

I = $420 - M. 

 

Plug in your new value for M, and you will find the interest.  If you got $60, then we got the same thing.