A first-class postage stamp now costs $0.50. If we assume an annual rate of inflation of 2.0%, in what year would you expect a stamp to cost $0.65?

To determine the year when a first-class postage stamp would cost $0.65, given an annual inflation rate of 2.0%, we can use the formula for compound interest:

\[
P_{\text{future}} = P_{\text{present}} \times (1 + r)^t
\]

Where:
- $ P_{\text{future}} $ is the future price of the stamp, which is $0.65.
- $ P_{\text{present}} $ is the current price of the stamp, which is $0.50.
- $ r $ is the annual inflation rate, which is 2% or 0.02.
- $ t $ is the number of years we need to find.

We need to solve for $ t $:

\[
0.65 = 0.50 \times (1.02)^t
\]

Dividing both sides by 0.50:

\[
\frac{0.65}{0.50} = (1.02)^t
\]

\[
1.3 = (1.02)^t
\]

Now, take the natural logarithm of both sides:

\[
\ln(1.3) = t \times \ln(1.02)
\]

Solving for $ t $:

\[
t = \frac{\ln(1.3)}{\ln(1.02)}
\]

Let me calculate this.It will take approximately 13.25 years for the price of a first-class postage stamp to increase from $0.50 to $0.65, assuming an annual inflation rate of 2.0%.

If we start counting from the current year, it would be expected to reach $0.65 in about 13 years and 3 months.

**Relative Questions:**

1. How does changing the inflation rate affect the time it takes for the stamp price to reach $0.65?
2. If the inflation rate were 3%, how many years would it take for the stamp to reach $0.65?
3. What would be the cost of the stamp after 20 years with a 2% inflation rate?
4. How would the time change if the starting price was $0.55 instead of $0.50?
5. What would be the price of the stamp in 15 years at the current inflation rate?

**Tip:** Understanding the impact of compound interest is crucial when considering long-term financial planning, as small changes in rates can lead to significant differences over time.

Learn how to predict when a first-class postage stamp will cost $0.65 using compound interest and an inflation rate of 2.0%. Understand the impact of inflation on long-term costs. Suitable for high school students and anyone interested in financial forecasting.

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