You expect to enroll in a four$-$year medical school six years from today, and you are planning accordingly. Current

tuition for medical school is $$61,000$ per year, and it's is expected to grow at a rate of $5\%$ per year in the future. How

much do you need to deposit in an investment account today, which earns $9\%$ per year, so that you can have enough

money to pay for medical school? You can assume tuition payments are due at the beginning of each year so that you

will have to make a tuition payment $6$ years from today, $7$ years from today, $8$ years from today and $9$ years from

today $($for a total of four tuition payments$).$

The amount of money you need to deposit in an account today is closest to:

A$.$ $$184,497$

B$.$ $$283,872$

C$.$ $$178,311$

D$.$ $$172,124$

And please show me how to do it mathmatically.