(e) In a bond agreement, the kingdom of Arendelle promises to pay coupons of $2,000 to the kingdom of Narnia at the end of each year forever (hence there is no maturity date or redemption value). The interest rate will depend on economic conditions as follows: The interest rates are 6%, 7%, 8% when the economic conditions are bad, normal, and good respectively. If the economy is bad this year, it must be normal next year. If the economy is good this year, then it must be normal next year. If the economy is normal this year, it has a probability of 0.8 to be bad, and a probability of 0.2 to be good next year. The first payment will start at the end of year 1, which has a normal economic condition. Suppose that both kingdoms will last forever, find the expected present value of this transaction. [8]