Please solve the following using these formulas and Maple:

the future value of a lumpsum A is L := (A, r, n, t) -> A*(1 + r/n)^(n*t); the future value of a stream of equal payments P is (with payments at the end of each period) S := (P, r, n, t) -> P*((1 + r/n)^(n*t) - 1)*n/r;

the Balance on a mortgage (or similar loan or annuity) is B := (A, r, n, t, P) -> A*(1 + r/n)^(n*t) - P*((1 + r/n)^(n*t) - 1)*n/r; The Value of a Bond is V := (F, R, r, n, T) -> F*R*(1 - (1 + r/n)^(-n*T))/r + F*(1 + r/n)^(-n*T);

where F is the facevalue, R the Coupon rate, r; the market rate (or `yield-to-maturity'), n the number of coupons per year, T the time to maturity.

Problem 2: Jack and Jill's problem: (10 pts) Jill loans Jack an amount X, and charges him 5% annual interest, compounded quarterly. Jack promises to pay back the loan with quarterly payments of $100 for 5 years, and then quarterly payments of $200 for 5 more years (a) estimate the amount X, using no technology.

(b) Find the exact amount using Maple

Problem 3: Fixing a flawed schedule (12 pts) Alice gives Bob a loan of $5,000 to be repaid by 10 annual payments of $600. Just after Bob makes his 5th payment, they discover that each of the 10 payments should have been 10% higher than originally scheduled. They agree that Bob will make increased payments of X in the 6th through 10th year to adjust for the error. Find X.

Problem 4: Implied interest rate (8 pts) Suppose a $5,000 loan is paid back in three annual installments of $1000 first, then $2000, and finally $3000. What is the implied interest rate?

Problem 5: One more mortgage problem (15 pts) Suppose you need a $200,000 mortgage to buy a house. The broker gives you a choice of a fixed-rate mortgage A and an adjustable-rate mortgage B The terms are as follows: (A) charges an annual rate - compounded monthly - of 7% for 30 years (B) charges an annual rate - compounded monthly - of 5% for the first 5 years, and then 10% for the remaining 25 years. Both are set up with a fixed monthly payment that pays off the mortgage in 30 years. Neither mortgages charges a fee for pre-paying the mortgage. (In other words, you can pay more than the minimum monthly payment).

Which mortgage you would pick and why?

Would your answer change if there was a good chance that you might move in 5 years?