An investment of $1000$ is to be used to make payments of $10$ at the end of the first year, $20$ at the end of the second year, $30$ at the end of the third year, etc., every year for as long as possible. A smaller final payment is paid one year after the last regular payment. The fund earns an effective rate of interest of $4\%.$

Calculate the amount of the smaller final payment $R.($Hint: By doing trial and error, one can find that the last full payment is made at the end of $17$ th year.$)$

$38$

$39$

$40$

$41$

$42$