Question

Deanna wants to borrow $8000. Two banks offer a 4-year loan term. One loan has a 5% interest rate, and the other has a 6% interest rate. How much more interest will Deanna pay if she accepts the loan at 6% for the 4-year term?

Answer 1

need some help

Answer 2

Yeah.

Answer 3

I think it is 0.75 percent

Answer 4

Thank you.

Answer 5

It seems like the question was asking for the amount of interest instead of a percentage

Answer 6

oh ok

Answer 7

let me see again

Answer 8

So they are asking for the amount that you will be paying in interest if you choose the bank that has 6% interest rate. We can use the interest rate formula. Let's call bank A at 5% and bank B at 6%.

\[I_A=Prt\]
and
\[I_B=Prt\]

in order to how much more you will be paying at 6% we need to subtract the bank A from bank B
\[I_B-I_A=I\]

Where I is the interest you will be paying more.

\[I_B-I_A=P(rt_B-rt_A)\]

P is the amount that is being borrowed, r is the interest rate and t is the time in years.


\[I_B-I_A=8000*(0.06(4)-0.05(4)) \]
\[I_B-I_A=8000*(0.24-0.04) \]
\[I_B-I_A=8000*(0.04) \]
\[I_B-I_A= 320\]

Since we let
\[I_B-I_A=I\]

We can say that
\[I=320\]

So at bank B you will be paying $320 if you were to barrow $ 8000.