To calculate the future value of a painting worth $135 that increases in value by 1.2% each year for 70 years, we can use the formula for compound interest:
\[ FV = P \times (1 + r)^n \]
where:
- \( FV \) is the future value,
- \( P \) is the present value (initial value),
- \( r \) is the annual interest rate (expressed as a decimal),
- \( n \) is the number of years the money is invested or grows.
For this case:
- \( P = 135 \)
- \( r = 1.2% = 0.012 \)
- \( n = 70 \)
Now, plugging in the values:
\[ FV = 135 \times (1 + 0.012)^{70} \] \[ FV = 135 \times (1.012)^{70} \]
Calculating \( (1.012)^{70} \):
\[ (1.012)^{70} \approx 2.2522 \]
Now we multiply this by the initial value:
\[ FV \approx 135 \times 2.2522 \approx 303.06 \]
So, the value of the painting after 70 years would be approximately $303.06.