Question

A car dealer sold 100 cars in his first year and plans to increase his sales by 10 percent each year for the next 5 years. How many cars will he have sold at the end of his fifth year?

Answer 1

To calculate the number of cars the dealer will sell at the end of the fifth year with an annual increase of 10%, we can use the formula for compound growth:

\[
\text{Future Value} = \text{Present Value} \times (1 + r)^n
\]

Where:
- Present Value = 100 (initial number of cars sold)
- \( r \) = 10% = 0.10 (the growth rate)
- \( n \) = 5 (the number of years)

Now we can calculate the future value:

\[
\text{Future Value} = 100 \times (1 + 0.10)^5
\]

Calculating \( (1 + 0.10)^5 \):

\[
(1.10)^5 = 1.61051 \quad \text{(approximately)}
\]

Now substituting this back into the equation:

\[
\text{Future Value} = 100 \times 1.61051 \approx 161.051
\]

Since the number of cars must be a whole number, we can round this to:

\[
\text{Future Value} \approx 161
\]

Thus, at the end of his fifth year, the dealer will have sold approximately **161 cars**.