The cost of a car four years ago was K21000. The cost of the car has now increased due to inflation to K22910. What has the rate of inflation been over the four years, assuming it is the same for each of the four years? Find the rate.
To find the rate of inflation over the four years, we can use the formula:
Rate of Inflation = ((Current Cost - Original Cost) / Original Cost) * 100
Given:
Original Cost = K21000
Current Cost = K22910
Rate of Inflation = ((K22910 - K21000) / K21000) * 100
Rate of Inflation = (K1910 / K21000) * 100
Rate of Inflation = 0.09095 * 100
Rate of Inflation = 9.095%
Therefore, the rate of inflation over the four years has been 9.095%.
Use the formula A equals P to the power of n, where A is the amount accumulated , P is the principle, and n is the time or term. Now find the correct answer.
Using the formula A = P(1 + r)^n, where:
A = K22910 (current cost)
P = K21000 (original cost)
r = rate of inflation
n = 4 years
We can plug in the values and solve for the rate of inflation:
K22910 = K21000(1 + r)^4
22910 / 21000 = (1 + r)^4
1.091 = (1 + r)^4
Taking the fourth root of both sides:
(1.091)^(1/4) = 1 + r
1.0218 = 1 + r
r = 1.0218 - 1
r = 0.0218
Converting the decimal to a percentage:
r = 0.0218 * 100
r = 2.18%
Therefore, the correct rate of inflation over the four years is 2.18%.