PLEASE PROVIDE A CORRECT ANSWER. I have posted this already and the answer is wrong, you will not get an upvote if u copy that wrong answer

Suppose r>0 describes an interest rate, and compounding interest is made according to the following scheme: After the first month we compound at an interest rate r, and after the third month we compound at an interest rate of r. After this, the cycle begins again. a. If R dollars is invested at the beginning of the year according to the above compounding scheme, determine the return after four years. b. Determine the Annual Percentage Rate s>0 such that if we compounded monthly at an APR of s, we would have the same return as the investment scheme above after one year. c. 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? d. If a perpetuity of R dollars is paid out every six months using the above compounding interest scheme, the present value of the perpetuity is A=(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