00:01
Michelle borrows a total of $5 ,000 in student loans from two lenders.
00:06
One charges 4 .6 % simple interest and the other charges 6 .2 % simple interest.
00:12
She is not required to pay off the principal or interest for three years.
00:16
However, at the end of the third year, she'll owe a total of 762 for the interest from both loans.
00:21
How much did she borrow from each lender? so we're going to let x be the loan at 4 .6%.
00:30
And then we're going to let 5 ,000 minus x be the loan at 6 .2%.
00:39
We're going to use the equation i equals p times r times t.
00:44
P is principal, r is the interest rate, and we're going to convert that percentage into a decimal, and then t is the time in years.
00:51
In this case, they're both three years.
00:53
So for the first one, we have x because we don't know the principle, times 0 .046, that's that 4 .6 % interest times the three years.
01:04
And this gives us 0 .138x.
01:08
For the second one, we have 5 ,000 minus x times 0 .062.
01:16
That's at 6 .2 % in decimal form times the three years.
01:20
This gives me i2 equals 5 ,000 minus x times 0 .186.
01:27
I'm going to do.
01:28
Distribute this 0 .186 and we get 930 minus 0 .186 x.
01:37
We know the total interest she owed after those three years is $762...