Question

You deposit $300 a month into an annuity at 4% to help save for retirement. You plan to make these deposits for 25 years. Assuming no other deposits or withdraws, how much will you have at the end of 25 years? Round to the nearest cent.

Answer 1

Answer: 154238.86

Explanation:

Answer 2

Given:

We deposit $300 a month into an annuity at 4% for 25 years.

To find:

The amount we have at the end of 25 years.

Step-by-step solution:

`\begin{gathered} End\text{ amount = Amount per year}*(((1+i)^n-1)/(i)) \\ i=rate\text{ of interest} \\ n=number\text{ of payments} \end{gathered}`

Putting the values in this formula:

Amount per month = $300

Amount per year = $300 × 12 = $3600

Annuality = 4%

`\begin{gathered} End\text{ amount = 3600}*((1+0.04)^(25)-1)/(0.04) \\ \\ End\text{ amount = 3600}*((1.04)^(25)-1)/(0.04) \\ \\ End\text{ amount = 3600}*(2.66-1)/(0.04) \\ \\ End\text{ amount = 3600}*(1.66)/(0.04) \\ \\ End\text{ amount = 3600}*\text{ 41.5} \\ \\ End\text{ amount = 1,49,400} \end{gathered}`

Thus we can say that after investing $300 a month for 12 years at 4% annuality, we got $1,49,400 at the end.