What amount will be paid out by the insurer for a partial loss of $10,000 given Betty's coinsurance penalty?

To determine the payout by the insurer for a partial loss of $10,000 given a coinsurance penalty, it is necessary to understand how coinsurance functions in property insurance. Coinsurance is a provision that requires the policyholder to insure their property for a specified percentage of its total value. If the policyholder fails to meet this minimum requirement, a penalty is applied when a claim is made.

To illustrate this, let's assume that in this scenario, the required coinsurance percentage is 80%. This means that Betty should have insured her property for at least 80% of its actual value. If the actual value is, for example, $50,000, Betty should have coverage of at least $40,000 (80% of $50,000).

If Betty only has $30,000 in coverage, she is underinsured and subject to a coinsurance penalty. To calculate the penalty, the amount she is actually insured (in this case, $30,000) is divided by the required amount (the 80% coverage, which is $40,000). This ratio calculates to 0.75 (or 75%).

When calculating payout for a partial loss, the actual loss is then multiplied by this ratio to find the