Three years ago the bus fare from Lae to Madang was K60. Now it is K80.
Calculate the average annual rate of inflation for the cost of fares from Lae to Madang over three years.
To calculate the average annual rate of inflation for the bus fare from Lae to Madang over three years, we can use the formula for annual rate of inflation:
Average annual rate of inflation = ((Current Price / Previous Price)^(1/Number of Years) - 1) * 100
Current Price (the fare now) = K80
Previous Price (the fare three years ago) = K60
Number of Years = 3
Average annual rate of inflation = ((80 / 60)^(1/3) - 1) * 100
= (1.3333^(1/3) - 1) * 100
= (1.1225 - 1) * 100
= 0.1225 * 100
= 12.25%
Therefore, the average annual rate of inflation for the cost of fares from Lae to Madang over three years is 12.25%.
Use the formula: Inflated value after 'n' years = PR^(n). Where
P is the amount accumulated after 'n' years.
R= 1+r/100
n is the terms or number of years.
Using the new formula provided:
Inflated value after 3 years = P(1 + r/100)^3
Given:
P = K80 (current fare)
r = average annual rate of inflation
n = 3 years
We want to find the value of r (average annual rate of inflation). We know that the inflated value after 3 years will be K80, given that the fare was K60 three years ago.
So, K80 = K60(1 + r/100)^3
Dividing both sides by K60, we get:
4/3 = (1 + r/100)^3
Taking the cube root of both sides:
(4/3)^(1/3) = 1 + r/100
1.098 = 1 + r/100
r/100 = 0.098
r = 9.8
Therefore, the average annual rate of inflation for the cost of fares from Lae to Madang over three years is 9.8%.
Use this formula: A=PR^(n), where:
A is the inflated value after 'n' years.
P is the principal.
R = 1+r/100
n is the terms or number of years.
Let's use the formula A = PR^n and the given information:
Initial fare (P) = K60
Current fare (A) = K80
Number of years (n) = 3 years
R = 1 + r/100
We want to find the average annual rate of inflation (r).
Using the formula A = PR^n:
K80 = K60 * (1 + r/100)^3
Divide both sides by K60:
80 / 60 = (1 + r/100)^3
4/3 = (1 + r/100)^3
Taking the cube root of both sides:
(4/3)^(1/3) = 1 + r/100
1.1547 = 1 + r/100
r/100 = 0.1547
r = 15.47
Therefore, the average annual rate of inflation for the cost of fares from Lae to Madang over three years is 15.47%.
I think the answer might be 33.3%
Let's go through the calculation again to confirm the average annual rate of inflation.
Using the formula A = PR^n and the given information:
Initial fare (P) = K60
Current fare (A) = K80
Number of years (n) = 3 years
R = 1 + r/100
We want to find the average annual rate of inflation (r).
Using the formula A = PR^n:
K80 = K60 * (1 + r/100)^3
Divide both sides by K60:
80 / 60 = (1 + r/100)^3
4/3 = (1 + r/100)^3
Taking the cube root of both sides:
(4/3)^(1/3) = 1 + r/100
1.2599 = 1 + r/100
r/100 = 0.2599
r = 25.99
Therefore, the average annual rate of inflation for the cost of fares from Lae to Madang over three years is 25.99%. This is slightly different from the 33.3% figure you mentioned.
Proof check your answer
Let's go through the calculation again to confirm the average annual rate of inflation using the formula provided:
Given:
Initial fare (P) = K60
Current fare (A) = K80
Number of years (n) = 3 years
R = 1 + r/100
Using the formula A = PR^n:
K80 = K60 * (1 + r/100)^3
Divide both sides by K60:
80 / 60 = (1 + r/100)^3
4/3 = (1 + r/100)^3
Taking the cube root of both sides:
(4/3)^(1/3) = 1 + r/100
1.2599 = 1 + r/100
r/100 = 0.2599
r = 25.99%
Therefore, the average annual rate of inflation for the cost of fares from Lae to Madang over three years is indeed 25.99%. Thank you for pointing out the error previously mentioned.