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The rate is the return on your investment. Since you'll receive 100\$ after 12 months, $\frac{100 - P}{P} = \frac{100 - 89.0}{89.0} = \frac{11}{89} = 12.36 \%$. Same for the 6-month T-Bill: $\frac{100 - P}{P} = \frac{100 - 94.0}{94.0} = \frac{6}{94} = 6.38 \%$.


Strictly speaking, any risk-free interest rate can be composed into three components: The rate expectations component is the market's "true" expectation for future interest rate. A bond risk premium component: longer maturity bonds have higher duration risk than cash. Accordingly market participants will demand more compensation for taking on duration ...


Do you want to model the returns in a risk-neutral framework (for derivatives) or in the real world measure (for risk analysis/portfolio construction)? For the first approach (say modelling under $Q$) you should go to the literature on bond and FX-derivatives. I would go more into detail if this is your aim. The formulation $N(\mu-\sigma^2/2,\sigma)$ ...

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