Solve manually using formulas/actuarial symbols. Show complete solutions.

1. Xia received an HMO card which allows her to reimburse all of her healthcare expenses. She had healthcare expenses of 100 per week for the first 50 weeks of the year. She sent in claim forms for all of her reimbursable expenses in bulk at the end of the 50th week and received payment at the end of the 51st week, which she deposited in her account on the same day that she received it.

Calculate the difference between the amount actually accumulated in her savings account at year end and the amount that could have been accumulated if Xia sent in her claim forms at the end of each week and received the payment at the end of the following week. Let the annual effective rate of interest = 10.95%.

2. Refer to the table below. Investment of $100 is made at the beginning of calendar years z, z+1 and z+2. The total amount of interest credited by the fund during the year z + 3 is $28.40. Compute for j.