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An investor bought a $63$-day Treasury bill with a face value of $\$105000$ to yield $3.55$%. The investor sold the T-bill $23$ days later to another investor who yields $2.8$%. What rate of return did the original investor realize?

So right off the start I find the $P$ by doing $$P = 105000/(1+0.0355(63/365)) = 104360.5415$$

Then $$S = 104360.5415(1+0.028(23/365)) = 104544.6734.$$

Rate of return would be = $(104544.6734-104360.5415)/(104360.5415)$

Can someone let me know what I'm doing wrong, thanks

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Your calculation for $S$ seems incorrect. The selling price should yield 2.8%, i.e. it should reach $105,000$ in the remaining $40$ days. So $S = \dfrac{105000}{(1 + 0.028 * 40 / 365)} = 104678.80$.

So the rate of return would be $\dfrac{S-P}{P} \times 100$, this is for $23$ days. Now annualise it., i.e multiply by $\frac{365}{23}$, so the final answer would be $\color{blue}{4.84 \%}$.

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    So would the rate of return be (104678.80 - P / P)*100? – 2017-01-07
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    The submitted answer was still incorrect. Any ideas? – 2017-01-07
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    Not sure what the answer is unfortunately. The answer I got was 0.30% but it is incorrect – 2017-01-07
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    Did you annualise it ? – 2017-01-07
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    No how do I do that? – 2017-01-07
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    I got it thank you so much!!! I just had to multiply the rate by (365/23). Thank you a million times! – 2017-01-07