Answer:
The prize in 2040 would be $1,293,986.
Step-by-step explanation:
We can calculate the annual increase rate as if it was a compound interest.
Then we have a period of 2017-1903=114 years, where the prize goes from $50 to $235,000.
We can then calculate this rate r as:
[tex]FV=PV(1+r)^n\\\\\\r=\sqrt[n]{\dfrac{FV}{PV}} -1\\\\\\r=\sqrt[114]{\dfrac{235,000}{50}} -1\\\\\\r=\sqrt[114]{4700} -1\\\\\\r=1.077-1\\\\\\r=0.077[/tex]
We can calculate then the prize, increasing at the same rate, from 2017 to 2040.
The number of periods is n=2040-2017=23.
Then we have:
[tex]FV=PV(1+r)^n\\\\FV=235,000(1.077)^{23}=235,000\cdot 5.5063=1,293,986[/tex]
The prize in 2040 would be $1,293,986.
