Answer:
$4.76 for next year
5.5 years required to reach top of $5 or 6th year from now to top $5
Explanation:
For first question,
initial price is $4.7
Now for formula of percentage, we have to find 1.36% of 4.7
Consider this 1.36% value as x
So, (x/4.7)x100 = 1.36
x = (1.36x4.7)/100
x = 0.063
Now, this x is the increment in previous price,
So, new price = 4.7 + x
New price = 4.7 + 0.063
= $4.763
For second question, we will use geometric series concept
In geometric series, their is a common ratio, which is ratio of two consecutive terms,
Since, every time increment in price is 1.36%, so this 1.36% is a common ratio
Formula for geometric series is
T(n) = ar^(n-1)
Now, T(n) is the term to be found or last term which is here $5
a is first term which is $4.7
r is common ratio which is 1.36% or 1.0136 to eliminate % sign
n is to be found
5 = (4.7) (1.0136)^(n-1)
5/4.7 = (1.0136)^(n-1)
Applying log on both sides
log (5/4.7) = log (1.0136)^(n-1)
0.026 = (n-1)log(1.0136)
0.026 = (n-1) * (5.86x10^-3)
n-1 = 4.43
n = 5.4 years
So, in 5.4 years, price will hit $5
So, 5.5 years price will top $5