Coinsurance Clauses: Daniela owns an office building insured for $300,000 under a commercial property insurance policy with an 80% coinsurance clause. The building sustains a $200,000 loss from fire in a reception area. The replacement cost for the building at the time of the fire is $500,000.

1. How much does the insurer pay?
2. If Daniela had insured the office building for $500,000 at the time of the fire how much would the insurer have paid?

Answer: Coinsurance required: .8($500,000) = $400,000

a) Insurer pays ($300,000/$400,000) x $200,000 = $150,000

b) If Daniela has a $500,000 policy, the coinsurance requirement is met and the full amount of the partial loss is paid: $200,000

I know these answers are correct but i have no idea why. Could someone please explain this to me?