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

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

For

A= $10280

P=8000

t=6

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

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%