Final answer:
Thornton should accept approximately $373,108 today for the right to his inheritance of $500,000 due in three years, based on a 10% personal discount rate compounded semiannually.
Step-by-step explanation:
To determine the amount that Thornton should accept today for the right to his inheritance in three years, we need to calculate the present value of his $500,000 inheritance using the given personal discount rate of 10% interest compounded semiannually. To do this, we will use the present value formula for compound interest:
Present Value = Future Value / (1 + r/n)nt
Where:
- Future Value is the amount of money in the future, which is $500,000 in Thornton's case.
- r is the annual discount rate, which is 10% or 0.10.
- n is the number of times interest is compounded per year, which is 2 for semiannual compounding.
- t is the number of years until the money is received, which is 3 years.
Substituting in the values we get:
Present Value = $500,000 / (1 + 0.10/2)2*3
Present Value = $500,000 / (1 + 0.05)6
Present Value = $500,000 / (1.05)6
Present Value = $500,000 / 1.340095
Present Value ≈ $373,108
Therefore, the closest value to the amount that Thornton should accept today for the right to his inheritance is $373,108.