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n October 2017 a pound of apples cost $1.43, while oranges cost $1.07. Two years earlier...

n October 2017 a pound of apples cost $1.43, while oranges cost $1.07. Two years earlier the price of apples was only $1.22 a pound and that of oranges was $0.93 a pound.

What was the annual compound rate of growth in the price of apples?

What was the annual compound rate of growth in the price of oranges?

If the same rates of growth persist in the future, what will be the price of apples in 2030?

If the same rates of growth persist in the future, what will be the price of oranges in 2030?

Solutions

Expert Solution

Price of Apples Price of Oranges
Oct-17 1.43 1.07
Oct-15 1.22 0.93
We will divide the Price of 2017 and 2015 to get our Compounding factor 1.43/1.22 1.07/0.93
1.17 1.15
Suppose Growth Rate Be x, there is a difference of 2 Years so, for two years
our growth comes out to be (1+x/100)*(1+x/100), we will do Squareroot
Doing Squareroot of 1.17, we will get 1.08
1+x/100 1.08
x/100 1.08-1
x/100 0.08
x 8
Our Apples Growth rate is 8 % PA.
Similiarly for Oranges we get
Suppose Growth Rate Be x, there is a difference of 2 Years so, for two years
our growth comes out to be (1+x/100)*(1+x/100)
Doing Squareroot of 1.15, we will get 1.07
1+x/100 1.07
x/100 1.07-1
x 7.00
Our Orange Growth rate is 7 %

Price of Apples in 2030, we have 2017 today, and our growth rate is to be compounded for 13 Years (2030-2017)

So our rates is 1.43 * (1.08) 13 (Current Apple Price * Compounding Factor n) n is no of years compounded

1.43 * 2.72

=3.88 Apple rate in 2030

Same for Oranges

13 Years Compounding on Current rate of 1.07 with 7 % Growth rate

1.07 * (1.07)13

1.07 * 2.41

2.5787 Orange Rate in 2030

jeff jeffy answered 2 years ago
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