Question: 1. The difference equation for the quarterly balance in an increasing annuity with interest compounded quarterly and money added at the end of each quarter

1. The difference equation for the quarterly balance in an increasing annuity with interest compounded quarterly and money added at the end of each quarter year is
yn = 1.008yn-1 + 1196, y0 = 37,780
and the solution of the difference equation is
yn = -149,500 + 187,280(1.008)n.
(a) What are the amount initially deposited into the annuity, the annual rate of interest, and the quarterly amount deposited into the annuity?
(b) Will the value of the annuity reach $100,000 after 7 years, 8 years, or 9 years?
2. The difference equation for the weekly balance in a decreasing annuity with interest compounded weekly and money withdrawn at the end of each week is
yn = 1.0005yn-1 - 200, y0 = 24,792
and the solution of the difference equation is
yn = 400,000 - 375,208(1.0005)n.
(a) What are the amount initially deposited into the annuity, the annual rate of interest, and the weekly amount withdrawn from the annuity?
(b) Will the annuity be depleted after 128 weeks or 138 weeks?

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