Question

You invest a single amount of $10,000 for 5 years at 10 percent. At the end of 5 years you take the proceeds and invest them for 12 years at 15 percent. How much will you have after 17 years?

Short answer

The investor will have $86,166.31 after 17 years.

Step-by-step solution

Identification of the required information

Present value (PV) = $10,000

Period (n₁) = 5 years

Period (n₂) = 12 years

Interest Rate (i₁) = 10%

Interest Rate (i₂) = 15%

Future value (FV) after 17 years

$$\begin{gathered} \text{FV}\mathbf{=}\text{PV}\times {\left(1+i_1\right)}^{n_1}\times {\left(1+i_2\right)}^{n_2} \\ \mathbf{=}\$10,000\times {\left(1+10\%\right)}^5\times {\left(1+15\%\right)}^{12} \\ \mathbf{=}\$86,166.31 \end{gathered}$$