ns The first payment was $3,000, and after that the payments 5) oin in six months. payment w lul ahnual payments begin- each year. Find the value of this perpetuity on January 1, ctive interest rate was 6% from January 1, 1988 through increased b January 1, 1996 and 4% thereafter. with payments in arithmetic progressions 1) Suppose what the following annuity symbols mean and calculate them to the the effective interest rate per interest period is 3%. effecti (1) Suppose that Describe nearest 1oo (a) (Ds)281 (b) ()s (c) (100,10a) 15 Payments of $5,000 are made into a fund at the beginning of each year for ears. The fund is invested at an annual effective rate of i. The interest en ted is reinvested at 10%. The total accumulated value at the end of the genera ten years is $100,000. Find i. 3) A perpetuity has annual payments. The first payment is for $320 and then ayments increase by $30 each year until they become level at $980. Find the value of this annuity at the time of the first payment using an annual effective interest of4%. (4) [calculus needed] Perpetuity X has level payments of $300 at the end of each year. Perpetuity Y also has end-of-year payments but they begin at $45 and increase by $45 each year. Find the rate of interest which will make the differ- ence in present values between these two perpetuities a maximum. (5) Bob deposits $11,000 at the beginning of each year for six years in a fund earning an effective annual rate of 7.5%. The interest from this fund can only be reinvested at an effective annual rate of 5%. Find the accumulated value of receives an eight-year annuity-immediate with monthly payments. The payment is $300 and payments increase by $6 each month. The payments eposted in an account earning interest at a nominal rate of 6% convertible Bob's investments at the end of thirteen years. first onthly. What is the balance in the account at the end of the eight years