Question

An asphalt road requires no upkeep until the end of 2 years when P20,000 will be needed for the repairs. After this, P30,000 will be needed for repairs at the end of each year for the next 5 years, then P40,000 at the end of each year for the next 5 years. Find the present value of the upkeep for the 12 years if money is worth 8 ¾%.

Answer 1

$i=8.75\%$ annually.

The present value will be

$P = 20\,000 \cdot (1.0875)^{-2} +30\,000 \cdot(\frac{1-(1.0875)^{-5}}{0.0875})(1.0875)^{-2} +40\,000 \cdot \cdot(\frac{1-(1.0875)^{-5}}{0.0875})(1.0875)^{-7} = 18\,390.805 + 99\,310.70 +87\,053.94 = 204\,755.445$