An investor pays $P$ for an annuity that provides $100$ at the beginning of each month for ten years. These payments are invested at a nominal annual interest rate of $12\%$ convertible monthly. Monthly interest payments are reinvested at a nominal annual interest rate of $6\%$ convertible monthly.

The annual yield rate over the ten$-$year period is $8\%$ effective. Calculate $P.$

Possible Answers

$9,600$

$9,650$

$9,700$

$9,750$

$9,800$