Answer:
72,91
Explanation:
the key to answer this question is to see that we can calculate the present value as a series of future payments valuated today, so there are two stages, the first one i going until 10 years and from ther is to infinity, so the present value can be solved as:
[tex]PV =P*\frac{1-(1+i)^{-n} }{i}+P*\frac{1}{i}*(1+i)^{-n}[/tex]
where [tex]a_{n}[/tex] is the present value of the annuity, [tex]i[/tex] is the interest rate for every period payment, n is the number of payments, and P is the regular amount paid. so applying to this particular problem.
keep in mind that [tex]P*\frac{1}{i}*(1+i)^{-n}[/tex] is the formula for calculating a perpeuity, it means the present value of a infinite future payments but look carefully at the expresion [tex](1+i)^{-n}[/tex] it means we are calculating a perpeuity which is located in the future and we compute it as money of today, so we have:
[tex]PV =8,75*\frac{1-(1+0.12)^{-10} }{0.12}+8,75*\frac{1}{0.12}*(1+0.12)^{-10}[/tex]
[tex]PV =72,91[/tex]
