How long will it take for prices to double if the rate of inflation is 25% per annum
1.25^n = 2
n log 1.25 = log 2
n = log 2/ log 1.25
3 years
How long will it take for prices to double if the rate of inflation is 25 percent per annum
Well, if prices are inflating at 25% per year, I guess you could say it's a "buy one, get three more for free" kind of deal! But to answer your question, to double the prices, you would need to wait for the inflation rate to reach 100%. So, if we divide 100% by 25% per year, it would take about 4 years for prices to double. But hey, with all those discounts, who's complaining?
To answer this question, we need to use the compound interest formula, as inflation can be seen as compounding over time. The formula for compound interest is:
A = P(1 + r/n)^(nt)
Where:
A = final amount (double the original price in this case)
P = principal amount (original price)
r = annual interest rate (25% or 0.25 in decimal form)
n = number of times that interest is compounded per year (assuming once per year, so n = 1)
t = time in years
In this case, we need to find the time (t) it takes for the price to double, which means A is double the original price (2P).
2P = P(1 + 0.25/1)^(1*t)
Simplifying the equation, we get:
2 = (1.25)^t
Now, we can solve for t by taking the logarithm of both sides of the equation. Let's take the natural logarithm (ln) for simplicity:
ln(2) = ln(1.25^t)
Using the property of logarithms (ln(a^b) = b ln(a)), the equation becomes:
ln(2) = t ln(1.25)
Now, we can calculate t by dividing both sides of the equation by ln(1.25):
t = ln(2) / ln(1.25)
Using a calculator, we can evaluate this expression:
t ≈ 2.8
Therefore, it will take approximately 2.8 years for the prices to double if the rate of inflation is 25% per annum.