1.ANZ is offering a product that pays out $3,000 quarterly from the end of Mar 2021 to the end of Dec 2030 with annual interest rate 6% compounded quarterly. (e.g. payment is made at the end of every March, June, September, and December.)

a.What's the price of this annuity on Jan 1, 2019? (15 points)

b.If an investor buys this annuity on July 1 of 2025, how much should the investor pay? (10 points)

c.An investor buys the same product on Jan 2020 and every time he receives the payment, he will immediately invest in a saving account that pays him 1% per quarter. How much will his saving account become at the end of 2035? (15 points)

d.Due to the overwhelming responses of the product offered, ANZ is going to offer another product that pays out $3000 at the commencement of each quarter from Jan 2019 to Dec 2022 (e.g. the first day of Jan, April, July, and October) with annual interest rate 8% compounded quarterly. You are planning to take a vacation in Japan at the beginning of 2023. The value of the payments at the beginning of 2023 is just enough to cover the expected expenditure of the vacation. How much is the vacation at the beginning of 2023? (10 points)