1. In each case find the value of the perpetuities at December 31, 2017 using 6% interest.

a) Payments of $30,000 per year starting on January 1, 2018.

b) Payments of $48,000 per year paid on December 31 starting in 2018.

c) Payments of $8,000 made every June 30 and December 31 starting in 2018.

d) Payments of $5000 made every two months starting on January 1, 2020.

e) Payments made continuously at the rate of $200,000 per year starting on March 31, 2019

2. Find the values of the following continuous annuities on October 31, 2017.

a) Payments at the rate of $100,000 per year made from November 1, 2017 to October 31, 2027. Use i=6.5%.

b) Payments at the rate of $250,000 per year made from November 1, 2010 to October 31, 2017. Use d=5%.

c) Payments at the rate of $500,000 per year made from April 1, 2019 to March 31, 2025. Use δ=6%.

d) Payments at the rate of $80,000 per month made from February 1, 2009 to January 31, 2015. Use i=4.5%.

e) Payments at the rate of $20,000 per month made for 10 years starting on July 1, 2012. Use δ=5%.