Answer:
$ 15,532,522.20
Step-by-step explanation:
Let r be the annual rate of increasing ( in percentage ),
Here, the winning amount on 1908, P = $ 150,
Number of years from 1908 to 2015, t = 107,
Thus, the winning amount in 2015,
![A=P(1+\frac{r}{100})^{107}](https://tex.z-dn.net/?f=A%3DP%281%2B%5Cfrac%7Br%7D%7B100%7D%29%5E%7B107%7D)
![=150(1+\frac{r}{100})^{107}](https://tex.z-dn.net/?f=%3D150%281%2B%5Cfrac%7Br%7D%7B100%7D%29%5E%7B107%7D)
According to the question,
A = $1,550,000,
![\implies 1550000 = 150(1+\frac{r}{100})^{107}](https://tex.z-dn.net/?f=%5Cimplies%201550000%20%3D%20150%281%2B%5Cfrac%7Br%7D%7B100%7D%29%5E%7B107%7D)
By graphing calculator,
![r\approx 0.09 = 9\%](https://tex.z-dn.net/?f=r%5Capprox%200.09%20%3D%209%5C%25)
Now, the number of years from 1908 to 2042, t = 134,
Hence, the winning amount in 2042,
![A=150(1+\frac{9}{100})^{134}=\$15,532,522.2034\approx \$ 15,532,522.20](https://tex.z-dn.net/?f=A%3D150%281%2B%5Cfrac%7B9%7D%7B100%7D%29%5E%7B134%7D%3D%5C%2415%2C532%2C522.2034%5Capprox%20%5C%24%2015%2C532%2C522.20)