Question

In 1895, the winner of a competition was paid $150. In 2006, the winner's prize was $70,000. What will the winner's prize be in 2040 if the prize continues increasing at the same rate?

Answer 1

Answer:

the price will grow to $ 507,571.77 If it continues with the same grow rate

Explanation:

first we solve for the rate:

2006 - 1895 = 111 years

$Nominal (1+r)^{n} = FV\\150 (1+r)^{111} = 70,000\\\\r = \sqrt[111]{70,000 / 150 } -1$

r =  0.06  

Now we apply this rate for the year 2040:

2040 - 2006 = 34 years

$Principal \: (1+ r)^{time} = Amount$

Principal 70,000.00

time 34.00

rate 0.06000

$70000 \: (1+ 0.06)^{34} = Amount$

Amount 507,571.77