The effective reserves at year 32 is -$23,614,073.02.
Here is the calculation of effective reserves at year 32:
Given:
Premium: $300,000
Duration: 35 years
Interest rate: 6% per annum
Claims paid: $300,000 in year 35
Calculation:
To ensure that the actual reserves in year 35 are zero, we need to adjust the claims paid in year 35. This can be done using the following formula:
Claims paid in year 35 = Premium * (1 + Interest rate)^(-Duration)
Plugging in the given values, we get:
Claims paid in year 35 = 300,000 * (1 + 0.06)^(-35) = $23,614,073.02
Therefore, the adjusted claims paid in year 35 is $23,614,073.02.
Now, we can calculate the effective reserves at year 32 using the following formula:
Effective reserves at year 32 = Premium * (1 + Interest rate)^(Duration - Year) - Adjusted claims paid in year 35
Plugging in the given values, we get:
Effective reserves at year 32 = 300,000 * (1 + 0.06)^(35 - 32) - 23,614,073.02 = -$23,614,073.02
Answer:
The effective reserves at year 32 is -$23,614,073.02. This means that the reserves are negative, indicating that the company has actually paid out more in claims than it has collected in premiums.