A one year consumer loan of $250,000 has a note rate of 5% and is valued at par on the
A one year consumer loan of $250,000 has a note rate of 5% and is valued at par on the balance sheet. The terms of the loan agreement are that in 6 months, the borrower must repay accrued interest to that point plus one-half of the principal. At the end of 12 months, the borrower repays remaining principal and accrued interest on the remaining balance. You fund this loan with a 6 month CD with an interest rate of 2% that pays interest at the end of 6 months when the instrument matures.
What is the duration of the loan?
If interest rates rise 25bps, what is the impact on the price of the loan? Show the equation using modified duration and provide an interpretation for full credit.
Which instrument—loan or CD shows greater price sensitivity to a change in interest rates for the same rate movement?