all questions please, and please do not use excel, I want to learn the process

11. A house loan of 200,000 is to be repaid with monthly payments of size X paid at the end of each month over a period of 30 years. The interest on the loan accumulates at a nominal annual rate of interest of 6% compounded monthly. Determine the amount of the monthly payments, X (round to nearest $0.01).. Suppose that in addition to the monthly payment of size X, the borrower pays an additional $100 per month starting with the first payment. i.e. they pay a total of X + $100 per month. How many payments will they need to make to pay off the loan (n will not be a whole number). a. b. 12. Suppose that an auto policy has Personal Injury Protection (PIP). PIP coverage pays for lost wages for a period of up to three years. In the first year, the benefit is $1000 per month. In the second year, the benefit is $1250 per month and in the third year, the benefit is $1500 per month. Assume a claim will pay the benefits for all three years (36 payments made at the end of each month). Assume that the interest rate is a nominal annual rate of 6%w compounded monthly (0.5% per month effective). Determine how much should be set aside today (at time t=0) to fully fund the claim. i.e find the present value at t= 0 of this string of 36 monthly payments 13. An estate sets up a trust to fund different charities. Each year, the fund will provide a payment of $10,000 at the end of each year to a selected charity. The fund earns an annual effective rate of interest of 5%. If the fund is to pay out in perpetuity, what must be the present value of the estate (i.e. find the present value of a perpetuity with payments of $10,000 and an interest rate of 5%). a. b. Suppose that charity A receives the payments in years 1, 4, 7, ...; charity B receives the payments in years 2, 5, 8, and charity C receives the payments in years 3, 6 ,9, . Determine the proportion of the estate that will be paid to charity B. (hint: the proportion would be the present value of charity B's payments divided by the present value of the estate) 14. A 20-year annuity-immediate with varying semi-annual payments is purchased (i.e. payments occur at the vend of each 6-month period). The first payment is equal to 1250. Beginning with the second payment, the payments start to increase. For payment 2 and all future payments, the current payment is 2.0% larger than the previous payment. At a nominal annual interest rate of 9.1%, compounded semi-annually, find the present value of the annuity. (This is called a geometric annuity. You can use our notation and the "real" rate of interest)