Question 4 please, with steps. Thanks.

4. (a) Emily and Mirabelle want to purchase an annuity due that makes 30 annual payments of SR. The annuity costs $20,983.40 using i = 5%. They agree that Emily will get the first 10 payments and pay $10,983,40 towards the cost. Mirabelle will receive the last 20 payments of the annuity and contribute $10,000 to purchase. Assuming an annual effective interest rate of / 5%, did they each pay their fair share? Justify your answer. (5) (b) As she receives them, Emily invests the payments from the annuity into a bank account earning interest at annual effective discount rate, d = 4% and leaves them there. Similarly, Mirabelle places all her payments into a bank account earning interest at force of interest 8.4 %. At some time T> 30, the accumulated values of their accounts are equal. Find T. (6)