Suppose that 6-month, 12-month, 18-month, 24-month, and 30-month zero rates are 3%, 3.2%, 3.4%, 3.5%, and 3.6% per annum with co
ntinuous compounding respectively. Estimate the cash price of a bond with a face value of 100 that will mature in 30 months and pays a coupon of 4.5% per annum semiannually.
1 answer:
Answer:
cash price: 102.78
Explanation:
In bond valuation, the investor would be willing to pay, at the most, the present value of the future income stream discounted at the required rate of return (or yield). Thus, the value of the bond can be determined as in working shown in file attached.
there is an inverse relationship between the yield of a bond and its price or value. The higher rate of return (or yield) required, the lower the price of the bond, and vice versa. However, it should be noted that this relationship is not linear, but convex to the origin.
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Answer: The loan was taken for 265 days.
We arrive at the answer as follows:
First we find the ratio of interest paid to the total loan amount to determine the interest rate:
Interest paid = $1,307
Loan Amount = $45,000
Since the interest rate calculated above is less than the annual interest rate at 4%, we conclude that the loan taken was for a period of less than one year.
We can determine the period for which the loan was taken as follows:
Let 'x' be the time for which the loan was taken.
We need to solve for x in the proportion below
0.04 : 365 :: 0.029044444:x
Solving we get,