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
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 $\color{blue}{4.84 \%}$.