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 ​%, 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.

Answer 1

Complete the following question:

Medical diagnostic imaging devices, jet engines, lighting products, and chemicals are just some of the products that a conglomerate corporation develops, manufactures, and markets. In 2013, the stock price increased by 34.83 percent, but it fell by 8.2 percent in 2014. If you bought $1,000 worth of social media stock in the beginning of 2013, it would be worth $ by the end of 2014.

0.02078330 is the answer.

Step-by-step instructions:

The geometric mean is found by multiplying the following numbers together:

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

+ 1

As a result of the question:

Rate 1(r1) = 0.082 for 2014 stock decline = 8.2 percent

Increase in stock in 2013 = 34.83 percent rate 2(r2) = 0.3483

The number of observations (n) is equal to two.

As a result, the geometric mean is calculated as follows:

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

[((1 + 0.082) (1 + 0.3483)) [((1 + 0.082) (1 + 0.3483)) [((1 + 0.082) (1 + 0.3483)) [ + 1

Sqrt[(1.082)(1.3483)] is the square root of the number Sqrt[(1.082)(1.3483)]. + 1

sqrt(1.4588606) - 1 sqrt(1.4588606) sqrt(1.4588606) sqrt

1.2078330 - 1 = 1.2078330 + 1 = 1.2078330 + 1 = 1.

equals 0.2078330

Answer 2

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.

Answer: 0.2078330

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