45.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

48. You wish to establish a scholarship fund for students at Clever College. The fund would pay an annual scholarship that would start at $5,000 awarded one year from now and increase by 3.5% per year forever. If the fund could earn an effective annual return of 6%, how much would you need to contribute to the scholarship fund today for it to be fully funded?

A) $205,000

B) $207,000

C) $210,000

D) $214,000

E) $200,000

49. Holly Daze has taken out a ten-month zero-coupon loan of $3,000. If the lender charges 7.2% per year compounded quarterly, what is the amount she must pay back at the end of the loan?

A) $3,183.81

B) $3,174.19

C) $3,044.93

D) $3,169.47

E) $3,180.00

50. You are considering two perpetuities which are identical in every way, except that perpetuity A will begin making annual payments of $P to you two years from today while the first $P payment for perpetuity B will occur one year from today. Suppose the annual rate of return is r. It must be true that the present value of perpetuity:

A) B exceeds that of A by the PV of $P for one year, i.e. $P/(1+r).

B) A is greater than that of B by $P.

C) A exceeds that of B by the PV of $P for one year, i.e. $P/(1+r).

D) B is greater than that of A by $P.

E) B is equal to that of perpetuity A.

Can someone please help me with these questions? Thanks in advance :)