Suppose r>0 describes an interest rate, and compounding interest, and compounding interest is made according to the following scheme: fter the first month we compound at an interest rate r, and after the third month we compound at an interest rate r. After this, the cycle begins again. 1. If R dollars is invested at the beginning of the year according to the above compounding scheme, determine the return after four years. 2. Determine the PR s>0 such that if we compounded monthly using an PRs, we would have the same return as the investment scheme above after one year. 3. If interest is applied according to the scheme above, how much money must you invest today to ensure that your investment is worth G dollars after four months? 4. If a perpetuity of R is paid out every six months using the above compounding interest scheme, the present value of the perpetuity is A=R(1+r)4+R(1+r)8+R(1+r)12+ Use the infinite geometric series formula to evaluate this series, and simplify your answer as much as possible