Questions: Suppose you invest 180 a month for 4 years into an account earning 9% compounded monthly. After 4 years, you leave the money, without making additional deposits, in the account for another 26 years. How much will you have in the end?

Solution Steps

Using the formula $FV_{annuity} = P \times \left( \frac{(1 + \frac{r}{12})^{12t_1} - 1}{\frac{r}{12}} \right)$, where $P = 180$, $r = 0.09$, and $t_1 = 4$ years, we get: $FV_{annuity} = 180 \times \left( \frac{(1 + 0.0075)^{12*4} - 1}{0.0075} \right) = 10353.73$

Using the compound interest formula $FV_{total} = FV_{annuity} \times (1 + \frac{r}{12})^{12t_2}$, where $FV_{annuity} = 10353.73$ and $t_2 = 26$ years, we get: $FV_{total} = 10353.73 \times (1 + 0.0075)^{12*26} = 106550.1$

Final Answer: