Answer :
To solve the problem, we need to calculate the value of [tex]\( A = 20000 \times (1.015)^{16} \)[/tex].
Let's break it down step-by-step:
1. Understand the components:
- The initial amount, or principal, is 20,000.
- The growth rate is 1.015. This represents a 1.5% increase.
- The number of periods, or years, is 16.
2. Use the formula for compound growth:
- The formula for compound interest or growth is given by [tex]\( A = P(1 + r)^n \)[/tex], where:
- [tex]\( P \)[/tex] is the principal amount (20,000 in this case),
- [tex]\( r \)[/tex] is the growth rate (0.015, because 1.5% increase implies 1.015 growth factor),
- [tex]\( n \)[/tex] is the number of periods (16 years here).
3. Calculate the power:
- First, calculate [tex]\( (1.015)^{16} \)[/tex].
- This involves multiplying 1.015 by itself 16 times.
4. Calculate the final amount:
- Multiply the initial amount (20,000) by the result from step 3.
5. Result:
- After performing these calculations, the final amount [tex]\( A \)[/tex] is approximately 25,379.71.
Therefore, after 16 years, the investment or growth would result in approximately 25,379.71.
Let's break it down step-by-step:
1. Understand the components:
- The initial amount, or principal, is 20,000.
- The growth rate is 1.015. This represents a 1.5% increase.
- The number of periods, or years, is 16.
2. Use the formula for compound growth:
- The formula for compound interest or growth is given by [tex]\( A = P(1 + r)^n \)[/tex], where:
- [tex]\( P \)[/tex] is the principal amount (20,000 in this case),
- [tex]\( r \)[/tex] is the growth rate (0.015, because 1.5% increase implies 1.015 growth factor),
- [tex]\( n \)[/tex] is the number of periods (16 years here).
3. Calculate the power:
- First, calculate [tex]\( (1.015)^{16} \)[/tex].
- This involves multiplying 1.015 by itself 16 times.
4. Calculate the final amount:
- Multiply the initial amount (20,000) by the result from step 3.
5. Result:
- After performing these calculations, the final amount [tex]\( A \)[/tex] is approximately 25,379.71.
Therefore, after 16 years, the investment or growth would result in approximately 25,379.71.
