Hello everyone,
In my economics class, we have learned how to determine the present value of an annuity by using Present Value Tables. However, these tables seem more suited for someone not interested in learning math, and I am trying by myself to determine the present value by using series.
Could someone please help me with the following question? I have arrived at an answer but it differs from the correct one. My work is shown below.
Thank you.
---
1. A Government of Canada has a face value of $100,000, consisting of a coupon rate of 8% which is paid semi-annually. The maturity date is 10 years from now. If the Market Interest Rate is 5% now, what would you pay for this bond?
---
Firstly, I separated the question in two parts: the principal and the interest. The calculated amount for the principal was correct, so my shown work will be quite brief.
Principal :
Market Interest Rate = 5%, \(\displaystyle i = \frac{0.05%}{2}\), n = 20
\(\displaystyle A = P(1 + {\frac{i}{m}})^n\)
\(\displaystyle P =\) $\(\displaystyle 61027.09\)
Interest:
Since the interest is $8000/year, then semi-annually, it would become $4000/6 months. Now, i would be 1.04 as well since it is for 6 months.
Therefore, the first payment would be \(\displaystyle \frac{4000}{1.04^{20}}\).
\(\displaystyle S_{20} = a_1\frac{r^{20} - 1}{r -1}\)
\(\displaystyle S_{20} = \frac{4000}{1.04^{20}}\frac{1.04^{20} - 1}{1.04 -1}\)
= $54361.30
However, the provided answer for the interest is $59356.55.
In my economics class, we have learned how to determine the present value of an annuity by using Present Value Tables. However, these tables seem more suited for someone not interested in learning math, and I am trying by myself to determine the present value by using series.
Could someone please help me with the following question? I have arrived at an answer but it differs from the correct one. My work is shown below.
Thank you.
---
1. A Government of Canada has a face value of $100,000, consisting of a coupon rate of 8% which is paid semi-annually. The maturity date is 10 years from now. If the Market Interest Rate is 5% now, what would you pay for this bond?
---
Firstly, I separated the question in two parts: the principal and the interest. The calculated amount for the principal was correct, so my shown work will be quite brief.
Principal :
Market Interest Rate = 5%, \(\displaystyle i = \frac{0.05%}{2}\), n = 20
\(\displaystyle A = P(1 + {\frac{i}{m}})^n\)
\(\displaystyle P =\) $\(\displaystyle 61027.09\)
Interest:
Since the interest is $8000/year, then semi-annually, it would become $4000/6 months. Now, i would be 1.04 as well since it is for 6 months.
Therefore, the first payment would be \(\displaystyle \frac{4000}{1.04^{20}}\).
\(\displaystyle S_{20} = a_1\frac{r^{20} - 1}{r -1}\)
\(\displaystyle S_{20} = \frac{4000}{1.04^{20}}\frac{1.04^{20} - 1}{1.04 -1}\)
= $54361.30
However, the provided answer for the interest is $59356.55.
