Question

An investor was afraid that he would become like King Lear in his retirement and beg hospitality from his children, so he purchased grain "tithes," or shares in farm output, for 800 pounds. The tithes paid him 78 pounds per year for 30 years. What interest rate did the he receive on this investment?

Answer 1

as far as I can read it, he bought £800 in shares, who knows how many, is irrelevant in this case, however we also know that he got £78 for 30 years, what was the rate?

well, we can nevermind the 30 years part and keep an eye that every year his earned interest was £78 flat, so we're looking at a simple interest rate, since it's not compounding, so let's reword all that

with an initial investment of £800 yielding £78 per year, what's the interest rate?

`~~~~~~ \textit{Simple Interest Earned} \\\\ I = Prt\qquad \begin{cases} I=\textit{interest earned}\dotfill & \pounds 78\\ P=\textit{original amount deposited}\dotfill & \pounds 800\\ r=rate\to r\%\to (r)/(100)\\ t=years\dotfill &1 \end{cases} \\\\\\ 78 = (800)((r)/(100))(1) \implies 78=8r\implies \cfrac{78}{8}=r\implies \stackrel{ \% }{9.75}=r`