Question

The answers are at the bottom of the picture. i have know idea how to start a problem like this one. Please show work on all parts to help me out. Thank you.

Exercise (8.12) Consider a 10-year loan of 1,000 with inflation protection. The loan agreement specifies a continuously compounded interest rate of 4%, and that the repayment amount will be adjusted by a factor equal to the value of a particular price index on the repayment date, divided by the value of that index on the date of the loan. Suppose that the value of the price index specified in the agreement is 201.9 on the date of the loan and 241.8 at the end of the loan's 10-year term. What is the repayment amount the lender receives? What was the real rate of return for this loan, and what was the nominal rate of return?! (Express your answers as continuously compounded rates.) Answers: 1,786.64 Real: 4% Nominal: 5.80%

Answer 1

Repayment amount the lender receives = [Loan amount*e^(r*T)]*price index at the end of the loan/price index at the beginning of the loan

r = interest rate; T = loan period

Repayment amount the lender receives =[1,000*e^(0.04*10)]*241.8/201.9 = [1,000*e^0.4]*241.8/201.9 = (1,000*1.491825)*241.8/201.9 = (1,491.825)*241.8/201.9 = 360,723.285/201.9 = 1,786.64

Repayment amount the lender receives is 1,786.64.

Real rate of return for this loan is 4% because it doesn't include adjustment for inflation.

Nominal rate of return = [(1+real rate of return)*(1+inflation rate)] - 1

inflation rate = [(price index at the end of the loan/price index at the beginning of the loan)^{1/Loan period}] -1 = (241.8/201.9)^1/10 - 1 = 1.1976^0.1 - 1 = 1.0182 - 1 = 0.0182 or 1.82%

Nominal rate of return = [(1+0.04)*(1+0.0182)] - 1 = (1.04*1.0182) - 1 = 1.058 - 1 = 0.058 or 5.80%