Question

At the end of each year, 10% interest is charged on a $500 loan. The interest applies to any unpaid balance on the loan, including previous interest.Select all the expressions that represent the loan balance after two years if no payments are made: 500+2⋅(0.1)⋅500500⋅(1.1)⋅(1.1)500+(0.1)+(0.1)500⋅(1.1)²(500+50)⋅(1.1)

Answer 1

We have the following:

Since it's two years, the interest rate applies twice, just like that

$(500)\cdot(1.1)\cdot(1.1)=500\cdot(1.1)^2=605$

Now we check each case

$\begin{gathered} 500+2\cdot\mleft(0.1\mright)\cdot500=600 \\ \text{FALSE} \\ 500\cdot\mleft(1.1\mright)\cdot\mleft(1.1\mright)=605 \\ \text{TRUE} \\ 500+\mleft(0.1\mright)+\mleft(0.1\mright)=500.2 \\ \text{FALSE} \\ 500\cdot\mleft(1.1\mright)^{2}=605 \\ \text{TRUE } \\ \mleft(500+50\mright)\cdot\mleft(1.1\mright)=605 \\ \text{TRUE} \end{gathered}$