1. A fund is built with annual deposits increasing by 1 from 1 to 10 and then decreasing by 1 to $0 at an annual effective interest rate of 5%. At the end of 19 years, the fund is used to purchase a 8-year annuity with level payment $X at an annual effective interest rate of 3% with the first payment 20 years from today.

Calculate X

2. Annie wants to accumulate $60500 in a fund at the end of 20 years. She plans to deposit $800+tX at the end of year t (t = 1,2,...,10) and $1500 at the end of last 10 years. The fund earns an annual effective interest rate of 6%.

Calculate X

Please show all work and do not use excel, thanks!