Question

Question: Beverly Hills started a paper route on January 1. Every three months, she deposits $550 in her bank account, which earns 8 percent annually but is compounded quarterly. Four years later, she used the entire balance in her bank account to invest in an investment at 7 percent annually. How much will she have after three more years?

Short answer

Answer

The future value of the investment after the three years is $12,809.83.

Step-by-step solution

Identification of the required information

Payment (PMT) = $550

Periods for quarterly compounding (n₁) = 16 (4 years*4 quarters)

Interest Rate for quarterly compounding (i₁) = 2% (8%/4)

Re-investment period (n₂) = 3

Re-investment rate (i₂) = 7%

Future value of investment after the three years (FV)

$$\begin{gathered} \mathit{F}\mathit{V}\mathbf{=}\mathit{P}\mathit{M}\mathit{T}\mathbf{\times }\left[\frac{{\left(1+i_1\right)}^{n_1+1}}{i_1}\right]\mathbf{\times }{\left(1+i_2\right)}^{{\mathbf{n}}_{\mathbf{2}}} \\ \mathbf{\$}\mathbf{550}\mathbf{=}\mathbf{\times }\mathbf{\left[}\frac{{\left(1+2\%\right)}^{\mathbf{16}\mathbf{+}\mathbf{1}}}{\mathbf{2}\mathbf{\%}}\mathbf{\right]}\mathbf{\times }{\mathbf{(}\mathbf{1}\mathbf{+}\mathbf{7}\mathbf{\%}\mathbf{)}}^{\mathbf{3}} \\ \mathbf{\$}\mathbf{12}\mathbf{,}\mathbf{809}\mathbf{.}\mathbf{83} \end{gathered}$$