Final answer:
To find the total present value of Mary's annuity and additional payment, we calculate each separately and sum them. The $500 payment in year 3 is discounted back three years, while the $300 annuity is treated as a deferred annuity, calculated at the start of year 6 and then discounted back to the present. The sum of both present values will provide the total present value of all payments.
Step-by-step explanation:
To calculate the present value of Mary's annuity and additional payment, we need to discount the future payments back to their present value using the formula for present value:
Present Value = (Future value) / (1 + Interest rate)number of years
For the $500 payment in year 3, we calculate the present value as follows:
Present Value of $500 = $500 / (1 + 0.06)3
For the 10 year $300 annuity starting in year 6, we need to treat it as a deferred annuity. Since the annuity payments are at the end of each period, we use the formula for a present value of an ordinary annuity:
Present Value of Annuity = PMT * [(1 - (1 + r)-n) / r]
First, we calculate the present value of the annuity at the start of year 6 (the year the annuity begins), and then discount it back five more years to the present:
Present Value of Annuity at Year 6 = $300 * [(1 - (1 + 0.06)-10) / 0.06]
Then, we discount that amount back to the present:
Present Value of Annuity = Present Value at Year 6 / (1 + 0.06)5
Adding both present values will give the total present value of all payments that Mary will receive. To find out which option (a, b, c, d, e) is correct, the calculations above need to be completed with accurate numerical results.