Question

If $\$30,000$ is deposited in a savings account at the end of each year and the account pays interest of $5\%$ compounded annually, what will be the balance of the account at the end of $10$ years ?

Answer 1

Find the balance of the account at the end of $10$ year:

Use the future value formula to find the balance:

$\begin{array}{rcl}\mathrm{Future}\mathrm{value}& =& \mathrm{PMT}\times \left\{\left[{\left(1+\mathrm{rate}\mathrm{of}\mathrm{interest}\right)}^n-1\right]÷\mathrm{rate}\mathrm{of}\mathrm{interest}\right\}\\ & =& \$30,000\times \left\{\left[{\left(1+0.05\right)}^{10}-1\right]÷0.05\right\}\\ & =& \$30,000\times \left\{\left[\left(1+0.62889\right)-1\right]÷0.05\right\}\\ & =& \$30,000\times 12.5779\\ & =& \$377,336.78\end{array}$

Hence, the balance of the account after $10$ years is $\$377,336.78$.