The City of Brandon is installing a new swimming pool in the municipal recreation

centre. Two designs are under consideration, both of which are to be permanent

$($i$.$e$.,$ lasting forever$).$ The first design is for a reinforced concrete pool that has a first

cost of $$1500000.$ Every $10$ years, the inner surface of the pool would have to be refinished and painted at a cost of $$200000.$

The second design consists of a metal frame and a plastic liner, which would have an

initial cost of $$500000.$ For this alternative, the plastic liner must be replaced every

$5$ years at a cost of $$100000,$ and every $15$ years the metal frame would need replacement

at a cost of $$150000.$ Extra insurance of $$5000$ per year is required for the plastic liner

$($to cover repair costs if the liner leaks$).$ The city$$s cost of long$-$term funds is $5$ percent.

Determine which swimming pool design has the lower present cost