Question

You pay off a debt of $800 by paying 16% of the remaining balance each month. Find a formula that gives the remaining debt D after t months D: =

Answer 1

We were given:

You paid off a debt of $800 by paying 16% of the remaining balance

That means that after each payment, you owe (100-16)% = 84% = 0.84

$D_0=800$

At zero month, we have:

$\begin{gathered} t=0 \\ D(0)=800 \end{gathered}$

At 1 month, we have:

$\begin{gathered} t=1 \\ D(1)=D_0\times(1-0.16)^{} \\ D(1)=800\times(1-0.16) \\ D(1)=800\times0.84 \\ D\mleft(1\mright)=128 \end{gathered}$

At 2 months, we have:

$\begin{gathered} t=2 \\ D(2)=D_0\times(1-0.16)^2 \\ D(2)=800\times(1-0.16)^2 \\ D(2)=800\times0.84^2 \\ D(2)=564.48 \end{gathered}$

The general formula to calculate the remaining debt after t months is given by:

$\begin{gathered} D(t)=D_0\times(1-0.16)^t \\ D(t)=D_0\times0.84^t \\ D(t)=D_0(0.84^{})^t \\ \\ \therefore D(t)=D_0(0.84)^t \end{gathered}$