Respuesta :
Answer:
$21.277 million
Explanation:
Data provided in the question:
Amount of lottery won = $35 million
Number of annual payments = 20
Amount of annual payment = $1.75 million
Interest rate = 6%
Now,
Present value of the payment = Payment × Present value factor
Also,
Present value factor = [1 + r]⁻ⁿ
Since the payment started immediately
Therefore,
Base year i.e n = 0
Thus,
we have
Year (n) Annual payment Present value
0 $1.75 million $1.75 million
1 $1.75 million $ 1.650943 million
2 $1.75 million $1.557494 million
3 $1.75 million $1.469334 million
4 $1.75 million $1.386164 million
5 $1.75 million $1.307702 million
6 $1.75 million $1.233681 million
7 $1.75 million $1.16385 million
8 $1.75 million $1.097972 million
9 $1.75 million $1.035822 million
10 $1.75 million $0.977191 million
11 $1.75 million $0.921878 million
12 $1.75 million $0.869696 million
13 $1.75 million $0.820468 million
14 $1.75 million $0.774027 million
15 $1.75 million $0.730214 million
16 $1.75 million $0.688881 million
17 $1.75 million $0.649888 million
18 $1.75 million $0.613102 million
19 $1.75 million $0.578398 million
Hence,
The present value of the winnings = ∑ Present value of payments
= $21.277 million
