Question

How much do you need to invest now at $5\%$per annum compounded monthly so that in 1 year you will have $\$10000$?

Short answer

We need to invest$\$9513$to get$\$10,000$at the end of 1 year.

Step-by-step solution

Step 1. Write the given information.

To invest now at 5% per annum

compounded monthly so that in 1 year you will have $10,000.

The formula of principle$p=\frac{A}{{\left(1+{\displaystyle \frac{r}{n}}\right)}^{nt}}$

Step 2. Find the principle.

$$\begin{gathered} p=\frac{10000}{{\left(1+{\displaystyle \frac{0.05}{12}}\right)}^{12·1}} \\ =\frac{10000}{{\left({\displaystyle \frac{12.05}{12}}\right)}^{12}} \\ =\frac{10000}{1.05116189788} \\ =9513.2824 \end{gathered}$$