A car company announced that it would offer five years of free maintenance after

Question

A car company announced that it would offer five years of free maintenance after purchase for its new models that adds regular maintenance service to the factory warranty. If the car will require $2,420 in average annual maintenance expenses for the next 5 years following the free maintenance period, calculate the annual 10-year equivalent shifted uniform series cost at 6% per year? A car company announced that it would offer five years of free maintenance after purchase for its new models that adds regular maintenance service to the factory warranty. If the car will require $2,420 in average annual maintenance expenses for the next 5 years following the free maintenance period, calculate the annual 10-year equivalent shifted uniform series cost at 6% per year?

Explanation / Answer

In the first five years, there is no cost and then for the next five years there is an annual cost of $2,420. Find the present value of this series and then find its annual gradient

PV = $2,420*((P/A, 6%, 10) -  (P/A, 6%, 5))

= 2420*(7.3600871-4.2123638)

= $7617.49

Find the annual 10-year equivalent shifted uniform series cost = $7617.49*(A/P, 6%, 10)

= 1034.97

= $1035 approximately.

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