1. John Wins $1,000,000 in a lottery and will be paid 20 equal annual installments of $50,000 with the first payment due today. A bank offers to exchange Johns winnings for perpetuity of $X per month with the first payment due today. Find the value closest to $X assuming a 10% effective rate of interest.
2. You have an annuity which pays $1,200 every two years. The first payment is two years from now and the last payment is ten years from now. You can trade that annuity for another annuity of equivalent present value, which pays $180 per quarter starting today. The interest rate for both annuities is 4% per annum convertible quarterly. If you took the second annuity, how many quarterly payments would you receive? The last payment may be less than $180 but not more than $180.