Question

If you want to earn $4\%$ annual simple interest on an investment, how much should you pay for a note that will be worth $\$18,500$ in $10$ months?

Answer 1

Compute the investment you should make for a note that will worth $\$18,500$ in $10$ months.

The equation used to find the simple interest is $\mathrm{I}=\mathrm{Pr}\frac{t}{12}$, where $\mathrm{I}$ is the amount earned , $\mathrm{P}$ is the investment, $\mathrm{r}$ is the interest rate and $\frac{\mathrm{t}}{12}$ is the time in years.

Substitute $\mathrm{I}$ as $\$18,500$ , $\mathrm{r}$ as $4\%$ and $\mathrm{t}$ as $10$ in $\mathrm{I}=\mathrm{Pr}\frac{t}{12}$ and simplify.

$$\begin{gathered} 4\%P\frac{10}{12}=18500 \\ \Rightarrow P=\frac{18500\times 12}{4\%\times 10} \\ \Rightarrow P=\frac{22200000}{40} \\ \therefore P=\$555000 \end{gathered}$$

Hence, the investment you should make for a note that will worth $\$18,500$ in $10$ months is $\$555000$.