A conglomerate corporation develops, manufactures, and markets a wide range of products, including medical diagnostic imaging devices, jet engines, lighting products, and chemicals. In 2013, the stock price rose %, and in 2014, the stock price declined %. If one purchased $1,000 of some social media stock at the start of 2013, its value would be $ at the end of 2014. Required:
Compute the geometric mean rate of return per year of the two-year period 2013-2014.

Complete question :

A conglomerate corporation develops, manufactures, and markets a wide range of products, including medical diagnostic imaging devices, jet engines, lighting products, and chemicals. In 2013, the stock price rose 34.83 %, and in 2014, the stock price declined 8.2%. If one purchased $1,000 of some social media stock at the start of 2013, its value would be $ at the end of 2014.

0.2078330

Step-by-step explanation:

The geometric mean is calculated using :

[((1 + r1)(1+r2)(1+r3)...(1+rn))^(1/n) ]- 1

From the question:

2014 stock decline = 8.2% = rate 1(r1) = 0.082

2013 stock increase = 34.83% rate 2(r2) = 0.3483

Number of observations (n) = 2

Hence, geometric mean:

[((1 + r1)(1 + r2))^(1/n)] - 1

[((1 + 0.082) (1 + 0.3483))^(1/2)] - 1

Sqrt[(1.082)(1.3483)] - 1

Sqrt(1.4588606) - 1

= 1.2078330 - 1

= 0.2078330

14.3

step-by-step explanation:

add all the numbers together.

9 + 12 + 15 + 16 + 17 + 17 = 86

now, divide 86 by how many numbers we have: 6.

86 / 6 = 14.3