I have a really stupid question. I'm trying to figure out how long it will take someone to pay off their credit debt. So this is what I'm given:
Someone owes $800
Have an annual interest rate of 12%
And they pay off $60 a month.
How many years will it take for them to pay off their debt? Can I just use a simply I=PRT formula to figure it out? I feel like I'm overthinking it.
First of all you have to use the monthly interest rate $i_{12}=\frac{0.12}{12}=\frac{i}{12}=0.01$
Then you set up an equation. The compounded loan (L) minus the sum of the compounded payments (annuities) is at most zero. Without the values the inequality is
$$L\cdot (1+\frac{i}{12})^{12\cdot n}-a\cdot \frac{(1+\frac{i}{12})^{12\cdot n}-1}{\frac{i}{12}} \normalsize \leq 0$$
We can use the equality for calculation and then solve for n. At the end we can regard the inequality.
$$L\cdot (1+\frac{i}{12})^{12\cdot n}-a\cdot \frac{(1+\frac{i}{12})^{12\cdot n}-1}{\frac{i}{12}}\normalsize = 0$$
Inserting the values and bring the negative term to the RHS.
$$800\cdot 1.01^{12\cdot n}=60\cdot \frac{1.01^{12\cdot n}-1}{0.01}$$
You can start by multiplying both sides by $0.01$
$$8\cdot 1.01^{12\cdot n}=60\cdot \left( 1.01^{12\cdot n}-1\right) = 60\cdot 1.01^{12\cdot n} -60 $$
Subtracting $8\cdot 1.01^{12\cdot n}$ and adding $60$ on both sides of the equation.
$$60=52\cdot 1.01^{12\cdot n} $$
Can you proceed?
