7) Show that the following relationships hold. a) vm ani = an+m] - Ami b) nt = 1+ an-11 (m) (m) a n 11 d) v'sn = (1 + i)n-t an] [10 points] =S 8) Solve the following equations of value. a) Paula wants to accumulate $10,000 at the end of 8 years by investing continuously over the period at payment rate $X per year. Find the smallest value for X that will achieve Paula's goal using i = 5%. b) On January 1, 2018 Will invests $10,000 to an account paying a 3.25% real return. i) Find Will's AV on December 31, 2019 given inflation of 2.27% in 2018 and 1.95% in 2019. ii) Find the inflation rate in 2020 if Will's accumulated value on December 31, 2020 is $11,450. c) Helen invests $500 every 3 months into an account paying i(4) 8%. When will her account balance be at least $10,000? [10 points) 7) Show that the following relationships hold. a) vm ani = an+m] - Ami b) nt = 1+ an-11 (m) (m) a n 11 d) v'sn = (1 + i)n-t an] [10 points] =S 8) Solve the following equations of value. a) Paula wants to accumulate $10,000 at the end of 8 years by investing continuously over the period at payment rate $X per year. Find the smallest value for X that will achieve Paula's goal using i = 5%. b) On January 1, 2018 Will invests $10,000 to an account paying a 3.25% real return. i) Find Will's AV on December 31, 2019 given inflation of 2.27% in 2018 and 1.95% in 2019. ii) Find the inflation rate in 2020 if Will's accumulated value on December 31, 2020 is $11,450. c) Helen invests $500 every 3 months into an account paying i(4) 8%. When will her account balance be at least $10,000? [10 points)