Finance questions help needed. Need to see proper equation for #1, 10, 12, 13, 15. Excel for 19 and 20

1.You are saving for the college education of your two children. They are three years apart in age; one will begin college 14 years from today and the other will begin 17 years from today. You estimate that the expenses for the oldest child (the one starting 14 years from today) will be $28,000 per year while the expenses for the other child will be $32,000 per year. Each child will attend for four years. The annual interest rate you can earn is 7% per annum. How much must you deposit each month to adequately fund the college fund if you begin making deposits in one month and the final deposit takes place on the day your first child leaves for college?

10. You are considering the purchase of a security that costs $4,400 today. It offers an 11% return per year, compounded quarterly. If you purchase the security, you would receive payments of $1,000 in 1 year, $2,000 in 2 years, and $x in 4 years. How much must x be for you to receive the promised return?

12. Suppose you are thinking about purchasing a machine that costs $100,000 and can produce $8,000 in after-tax cash flow per year. The risk associated with this product corresponds to a 12% discount rate. How many years must the machine last for you to break even on this investment?

13.You are considering an annuity that would pay you $6,000 every three years. The

annuity would make 15 payments and the first payment would occur in 2 years

(e.g., the payments would occur at t=2, 5, 8,). If the interest rate associated with

this annuity is 7.5% per annum, what is the present value of this annuity?

15. What is the present value of a perpetuity that pays you $200 every other year if the first payment is to be made in 3 years and the appropriate discount rate is 7% p.a.?

You are purchasing a home that costs $430,000. You will make no down payment. Your bank has offered you a 30-year loan with monthly payments at a rate of 4.6% per annum.

19. Most banks require a borrower to pay private mortgage insurance (PMI) if he/she puts less than 20% down on a home loan. Most times, this means the borrower has to pay 1% of the loan amount per year (in the form of a monthly payment) until he has paid off 20% of the loan. Consider a borrower who has enough money ($86,000) to make a 20% down payment. If the borrower has the option to invest in a mutual fund that pays 9% per year, should he make the down payment or invest the $86,000 in the mutual fund? (Hint: think about all of the ramifications of the down payment decision: payment amount, reinvestment of difference, etc.).

20. Suppose you are given the option to refinance your mortgage after your make the 85th payment. If you refinance the loan, you would be taking out a loan for the current balance of your original loan (e.g., your answer from #11). The new loan is a 30-year loan with monthly payments at a 4.2% interest rate. You would also need to pay a $2,000 fee immediately. As in #19 above, you have the option to invest in a mutual fund that pays 9% per year. Should you refinance your loan?