Answer to Question #99805 in Financial Math for fatima

Question

Q2) You can obtain a loan of $100,000 at a rate of 10 percent for two years. You have a choice of i) paying the interest (10 percent) each year and the total principal at the end of the second year or ii) amortizing the loan, that is, paying interest (10 percent) and principal in equal payments each year. The loan is priced at par.


a. What is the duration of the loan under both methods of payment?


b. Explain the difference in the two results?

Answer 1

a. i) PV of CF x t for two years is: PV = 10,000/1.1*1 + 110,000/1.1^2*2 = 190,909.09.

Duration = PV/P = 190,909.09/100,000 = 1.91.

ii) PV of CF x t for two years is: PV = 57,619.05/1.1*1 + 57,619.05/1.1^2*2 = 147,619.05.

Duration = PV/P = 147,619.05/100,000 = 1.48.

b. Duration decreases dramatically when a portion of the principal is repaid at the end of

year one. Duration often is described as the weighted-average maturity of an asset. If more weight is given to early payments, the effective maturity of the asset is reduced.