Final answer:
The net premium policy value at time 10 can be calculated using the present value formula, taking into account the death benefit payable at the end of each quarter year. The formula is PV = DB/(1 + r)^n, where PV is the present value, DB is the death benefit, r is the quarterly interest rate, and n is the number of quarters.
Step-by-step explanation:
The net premium policy value at time 10 can be calculated by considering the death benefit payable at the end of each quarter year. To calculate the net premium policy value, we need to determine the present value of the death benefit at time 10, discounted at the quarterly interest rate. The formula to calculate the present value of the death benefit is:
PV = DB/(1 + r)^n
Where:
- PV = Present Value of the death benefit
- DB = Death Benefit
- r = Quarterly interest rate
- n = Number of quarters
Substituting the given values into the formula, we get:
PV = 500,000/(1 + r)^40
Since the time period is 10 years, and there are 4 quarters per year, the total number of quarters is 40. The quarterly interest rate can be calculated by dividing the annual interest rate by 4. Let's assume the annual interest rate is 6%:
Quarterly interest rate = 6%/4 = 1.5%
Substituting the values into the formula, we get:
PV = 500,000/(1 + 0.015)^40
Using a financial calculator or spreadsheet software, we can calculate the net premium policy value at time 10.