Question

Callum invests £800 in an account which offers

4% simple interest per year.
After 2 years he takes the money out. He reinvests
half of it in another account, which offers 5% simple
interest per year. He leaves it there for 10 years.
How much interest will Callum have gained in total
from his investments in these two accounts?

Answer 1

well, let's take a peek at the first investment part

`~~~~~~ \textit{Simple Interest Earned} \\\\ I = Prt\qquad \begin{cases} I=\textit{interest earned}\\ P=\textit{original amount deposited}\dotfill & \pounds 800\\ r=rate\to 4\%\to (4)/(100)\dotfill &0.04\\ t=years\dotfill &2 \end{cases} \\\\\\ I = (800)(0.04)(2) \implies I = 64`

so he got 64 bucks from that one, now the whole accumulated amount is 800 + 64 = £864, half of that is £432, now let's plug that in at 5% for 10 years.

`~~~~~~ \textit{Simple Interest Earned} \\\\ I = Prt\qquad \begin{cases} I=\textit{interest earned}\\ P=\textit{original amount deposited}\dotfill & \pounds 432\\ r=rate\to 5\%\to (5)/(100)\dotfill &0.05\\ t=years\dotfill &10 \end{cases} \\\\\\ I = (432)(0.05)(10) \implies I = 216 \\\\[-0.35em] ~\dotfill\\\\ \stackrel{ \textit{total interest earned} }{64~~ + ~~216\implies \text{\LARGE 280}}`