Question

Question HelpGil borrows $8,000 for college expenses. He will pay a total of $10,280 after 6 years. Gil says theinterest rate is at least 5%. Is he correct? Explain.Gil is(Type integers or decimals.)He will pay $ in interest, which corresponds to an interest rate of %.

Answer 1

Simple interest can be calculated as

`A=P(1+rt)`

Where

A is the accrued amount (final amount)

P is the principal amount

r is the interest rate expressed as a decimal value

t is the time period

You have to calculate the interest rate of the loan Gil borrowed.

First step is to write the equation for r

`\begin{gathered} A=P(1+rt) \\ (A)/(P)=1+rt \\ (A)/(P)-1=rt \\ ((A)/(P)-1)\cdot(1)/(t)=r \end{gathered}`

For

A= $10280

P=8000

t=6

`\begin{gathered} r=((10280)/(8000)-1)\cdot(1)/(6) \\ r=0.0475 \end{gathered}`

The interest rate is 0.0475, if you multiply it by 100 you get that it is 4.75%

To calculate the Interest, you have to subtract the money he borrowed (P) from the money he payd (A)

`\begin{gathered} I=A-P \\ I=10280-8000 \\ I=2280 \end{gathered}`

So he will pay $2280, which corresponds to an interest rate of 4.75%