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

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

Step-by-step 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