5) Solve the following annuity problems. a) An investor deposits $1000 to an account every December 31 starting in 2005. If the account earns 7.5% from 2005-10 and 6% thereafter, find the accumulated value at December 31, 2017. b) An insurer expects payments of $500m made at the end of each year for the next 25 years. Find the present value assuming interest of 5% for the next 10 years and 3% after 5 years. c) Payments of $300 are made at the end of every year, starting in one year and continuing forever. Find the present value of the payments using 6% interest for the first 10 years and 4.5% thereafter. d) Payments are due at the end of each year for 15 years. The payments start at $50 and increase by 5% every year. Find the present value at the start of the first year, using 6% interest for the first 5 years and 4% thereafter.