Answer:
It will take 71,35 months, wich can be rounded to 72, or 6 years
Step-by-step explanation:
The debt will be paid when [tex]b_{n} = 0[/tex], the formula can be written as:
[tex]b_{n} = b_{0} r^{n} - R (\frac{1-r^{n} }{1-r} ) = 0[/tex]
Solving for n:
[tex]\frac{R}{1-r} = \frac{b_{0}r^{n}}{1-r^{n} } = \frac{b_{0}r^{n}}{r^{n}(\frac{1}{r^{n} } -1) }[/tex]
[tex]\frac{1}{r^{n}} = \frac{b_{0}(1-r)}{R}+1= 0,28[/tex]
[tex]r^{n}= \frac{1}{0,28} = 3,5714[/tex]
Solving the exponential equation:
[tex]r^{n} = 3,5714 => n = log_{r} (3,5714) = \frac{log(3,5714)}{log(r)} =71,35[/tex]
It will take 71,35 months, wich can be rounded to 72, or 6 years
