To calculate the total amount after 5 years with an initial amount of $42 and an annual increase of 12%, you can use the formula for compound interest:
\[ A = P(1 + r)^n \]
Where:
- \( A \) is the amount of money accumulated after \( n \) years, including interest.
- \( P \) is the principal amount (the initial amount of money).
- \( r \) is the annual interest rate (decimal).
- \( n \) is the number of years the money is invested or borrowed.
In your case:
- \( P = 42 \)
- \( r = 0.12 \) (12%)
- \( n = 5 \)
Now plug in the values:
\[ A = 42(1 + 0.12)^5 \]
\[ A = 42(1.12)^5 \]
Calculating \( (1.12)^5 \):
\[ (1.12)^5 \approx 1.7623 \]
Now, multiply that by 42:
\[ A \approx 42 \times 1.7623 \approx 74.00 \]
So, the total amount after 5 years will be approximately $74.00.