Question

1.You want to finance a car for $25,000. You agree to a 5 year loan with a monthly interest rate of 0.55 percent. What is your required monthly payment?

2.How are bond prices and interest rates related? Use the terms 'discount', 'par', and 'premium' in your explanation.

Answer 1

(1 ): Monthly payment = $490.33 as follows:

(2). Price of the bond is the sum of present values (PVs) of all future cash flows. Future cash flows consist of periodical interest payments (coupon payments) and redemption of principal. These future cash flows are fixed. PVs are calculated by discounting the cash flows with the interest rate expected on reinvestment (Yield to maturity or YTM) as discount rate, for the time left till date of receipt of the cash flows. Hence, when the YTM (the discount rate) increases, amount of discount on future cash flows increases and as a result, the present values decreases. This result in decrease the bond price.

The reverse process takes place in case the market interest rates (yield) decrease after making the investment. In such a situation, price of the security increase when the market interest rate decreases.

As a result, if the interest rate in the market is higher than the coupon rate, price will be less than face value (bond at discount). On the reverse, if the interest rate is lower than the coupon rate, price of the bond will be higher than the face value (bond at a premium). In case both the interest rate expected and the coupon rate are equal, price of the bond will be equal to face value. Such bonds are called ‘at par’.