Please show the work/formulas.

Problem 26.30 | 3.570 At an annual effective interest rate of i, the present value of a perpetuity- immediate starting with a payment of 200 in the first year and increasing by 50 each year thereafter is 46,530. Calculate i. Problem 27.1 1825.596 A 20 year increasing annuity due pays 100 at the start of year 1, 105 at the start of year 2, 110 at the start of year 3, etc. In other words, each payment is $5 greater than the prior payment. Calculate the present value of this annuity at an annual effective rate of 5%. Problem 27.2 18333.33 A perpetuity pays 1000 at the beginning of the first year. Each subsequent payment is increased by inflation. If inflation is assumed to be 4% per year, calculate the present value of this perpetuity using an annual effective interest rate of 10%. Problem 27.6 785.40 You buy an increasing perpetuity-due with annual payments starting at 5 and increasing by 5 each year until the payment reaches 100. The payments remain at 100 thereafter. The annual effective interest rate is 7.5%. Deter- mine the present value of this perpetuity. Problem 27.7 23.32 Debbie receives her first annual payment of 5 today. Each subsequent pay- ment decreases by 1 per year until time 4 years. After year 4, each payment increases by 1 until time 8 years. The annual interest rate is 6%. Determine the present value