Final answer:
To find the present values of the shares of a, b, and c from the estate, we use the present value formula PV = P / (1 + r)^n, where P is each payment, r is the interest rate, and n is the year of payment. By calculating the present value of each recipient's share and adding them together, we ensure the total is equal to the original investment of 1,000,000 at a 5% interest rate.
Step-by-step explanation:
To determine the present values of the shares of a, b, and c from the 1,000,000 estate invested at an annual interest rate of 5%, we apply the present value concept. A receives 125,000 each year for 5 years. The present value (PV) of these payments is calculated using the formula PV = P / (1 + r)^n, where P is the payment, r is the discount rate (same as the interest rate in this context, 5%), and n is the number of years until the payment. For b, the same approach is used for annual payments of 75,000.
C receives the interest, which would be 50,000 each year (1,000,000 at 5%). The present value of these interest payments is also calculated using the same formula. The total present value is the sum of the present values of a, b, and c's shares. To verify that it sums up to 1,000,000, add the present value of a, b, and c. Since this is an equal interest rate scenario and the payments match the interest rate on the principal, the sum should naturally return to 1,000,000, thus verifying the calculation.