Question
you are offered two bonds, a on year Rwandan treasury bond with a yield to maturity of 9% and a one year Rwandan treasury bill with a yield on discount basis of 8.9%. which would you rather own? why?
Answers
GPT-4o mini
To make a decision on which investment to choose between the one-year Rwandan treasury bond with a yield to maturity (YTM) of 9% and the one-year Rwandan treasury bill with a yield on a discount basis of 8.9%, we need to compare their effective yields.
1. **Treasury Bond Yield**: The YTM of the treasury bond is 9%. This is the annualized return on the bond if held until maturity.
2. **Treasury Bill Yield**: The yield on the treasury bill is given on a discount basis. To convert the discount yield into an effective yield, we can use the formula for the effective yield of a T-bill:
\[
\text{Effective yield} = \frac{\text{Discount yield}}{1 - \text{Discount yield}}
\]
In this case, the discount yield is 8.9%, or 0.089. Therefore:
\[
\text{Effective yield} = \frac{0.089}{1 - 0.089} = \frac{0.089}{0.911} \approx 0.0978 \text{ or } 9.78\%
\]
**Comparison**:
- The yield on the treasury bond is **9%**.
- The effective yield on the treasury bill is approximately **9.78%**.
Given that the effective yield of the treasury bill (9.78%) is higher than the yield to maturity of the treasury bond (9%), you would likely prefer to own the **one-year Rwandan treasury bill**, as it offers a higher return on your investment over the one-year period.
1. **Treasury Bond Yield**: The YTM of the treasury bond is 9%. This is the annualized return on the bond if held until maturity.
2. **Treasury Bill Yield**: The yield on the treasury bill is given on a discount basis. To convert the discount yield into an effective yield, we can use the formula for the effective yield of a T-bill:
\[
\text{Effective yield} = \frac{\text{Discount yield}}{1 - \text{Discount yield}}
\]
In this case, the discount yield is 8.9%, or 0.089. Therefore:
\[
\text{Effective yield} = \frac{0.089}{1 - 0.089} = \frac{0.089}{0.911} \approx 0.0978 \text{ or } 9.78\%
\]
**Comparison**:
- The yield on the treasury bond is **9%**.
- The effective yield on the treasury bill is approximately **9.78%**.
Given that the effective yield of the treasury bill (9.78%) is higher than the yield to maturity of the treasury bond (9%), you would likely prefer to own the **one-year Rwandan treasury bill**, as it offers a higher return on your investment over the one-year period.