The grand prize in the OMG Lottery is a choice between $$1,000$ paid at the beginning of each month for a period of $10$ years and a lump sum paid immediately. If you can invest at an effective annual interest rate of $5\%,$ what is the minimum lump sum you would be willing to accept as winner of this lottery?

A$)$ $$94,766$

B$)$ $$95,152$

C$)$ $$94,282$

D$)$ $$94,675$

E$)$ $$93,847$

The correct answer is b$).$ Please do not use excel and explain the steps.