Question

state lottery payout provides 1.4 million to be paid in 25 installments of 56,000 per payment. the first 56,000 payment is immediate and the remaining 24 payments of 56,000 each will occur at the end of the next 24 years. if 7% is the discount rate, what is the present value of this stream of cash flows?
if 14% is the discount rate, what is the present value of the cash flow?

a. if 7% is the discount rate, the present value of the annuity due is $__. (round to the nearest cent)

Answer 1

Part 1: Present value of given stream of cash flows at 7% is computed as follows-

Formula sheet is given below-

Part 1: Present value of given stream of cash flows at 14% is computed as follows-

Formula sheet is given below-

Present value of annuity due is computed as follows-

Present value of annuity due = Periodic payment +{Periodic payment × [{1 – (1 + r)^{-(n - 1)}} / r]}

= 56,000 + 56,000 × [{1 – (1 + 0.07)^{-(25 - 1)}} / 0.07]

= 56,000 + {56,000 × 11.469334}

= 56,000 + 642,282.70

= 698,282.70