please answer all questions with work

4,5,6 and 7

4. (1 point) Say that 10 years from now, the first payment of a perpetual annual stream of cash flows worth $10,000 each will occur. The appropriate interest rate is 6 percent, annually compounded. What is the value of this cash flow stream in today's dollars? Show your work using the mathematical equations. Hint: use a timeline and recall that when we calculated the PV of a perpetuity at time 0, the first payment occurred at time 1. 5. (2 points) A bank will lend you $5,000 today with terms that require you to pay off the loan in 24 monthly installments of $250 each. What is the effective annual rate (EAR) of interest the bank is charging you? 6. (3 points) An insurance company is offering a new policy to its customers. Typically, the policy is bought by a parent for a child at the child's birth. The details of the policy are: The parent makes the following three payments to the insurance company: First birthday: $1,800 Second birthday: $1,900 Third birthday: $2,000 After the child's third birthday, no more payments are made. When the child reaches age 50, he or she receives $100,000. If the relevant interest rate is 6 percent, monthly compounded, is the policy worth buying? Show your work using the mathematical equations. 7. (4 points) You are buying your first home: a condo in the Central West End. You have found a 5 bedroom, 4 bathroom condo and have just signed the paperwork purchasing the home for $689,900. You made a down payment of $80,000 and are financing the remaining $609,900 with a 30-year mortgage loan. You will owe interest of 4.75% per year, monthly compounded. You will make equal monthly payments. Fill in the boxes of the following amortization schedule for your first payment period. Round your final answers to the nearest cent, but maintain at least 4 decimal places in your intermediate calculations, Show ALL your work. E Period Beginnin B Balance Monthly Payment Interest Repayment of Principal Ending Balance Points Possible: 1 1 1 1 Month 1 S609,900