Answer :
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:
[tex]\begin{gathered} End\text{ amount = Amount per year}\times(\frac{(1+i)^n-1}{i}) \\ i=rate\text{ of interest} \\ n=number\text{ of payments} \end{gathered}[/tex]
Putting the values in this formula:
Amount per month = $300
Amount per year = $300 × 12 = $3600
Annuality = 4%
[tex]\begin{gathered} End\text{ amount = 3600}\times\frac{(1+0.04)^{25}-1}{0.04} \\ \\ End\text{ amount = 3600}\times\frac{(1.04)^{25}-1}{0.04} \\ \\ End\text{ amount = 3600}\times\frac{2.66-1}{0.04} \\ \\ End\text{ amount = 3600}\times\frac{1.66}{0.04} \\ \\ End\text{ amount = 3600}\times\text{ 41.5} \\ \\ End\text{ amount = 1,49,400} \end{gathered}[/tex]Thus we can say that after investing $300 a month for 12 years at 4% annuality, we got $1,49,400 at the end.
