A borrower and a lender agree on a loan of value L. A year later, the borrower pays back 32L(1+x) two years later, the borrower pays back 3L(1+x)2 What is the interest rate (yield to maturity) of this loan? Let's try to prove the following claim: a coupon bond's price (P) and face value (F) are equal if and only if the coupon rate (c) and the interest rate defined as the yield to maturity (i) are equal, regardless of the time remaining to maturity. Recall the formula: P=1+icF++(1+i)ncF+(1+i)nF, where cF is the coupon payment. (a) Suppose there is only one year left to maturity (n=1). Show that if i=c, then P=F. Also show that if P=F, then i=c. (b) Show or argue that the same is true for any n>1