“at time zero is equal to $121.00. calculate gdp 15 years later if the annual”
“At time zero is equal to $121.00. Calculate GDP 15 years later if the annual growth rate is X%”
Answer:
To calculate GDP 15 years later with an annual growth rate, you’ll use the formula for compound interest:
\text{Future GDP} = \text{Initial GDP} \times (1 + r)^t
Where:
- Initial GDP is $121.00.
- r is the annual growth rate (expressed as a decimal).
- t is the time in years, which is 15 in this case.
Step-by-Step Calculation:
-
Convert the Growth Rate: Let’s assume the growth rate is X%. Convert this percentage to a decimal by dividing by 100: r = \frac{X}{100}.
-
Apply the Formula: Insert the values into the formula.
$$\text{Future GDP} = 121 \times (1 + \frac{X}{100})^{15}$$
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Calculation Example: If the growth rate is, for example, 3%, plug in the values:
$$\text{Future GDP} = 121 \times (1 + \frac{3}{100})^{15}$$
Compute further:
$$\text{Future GDP} = 121 \times (1.03)^{15}$$
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Solve the Expression: Use a calculator to find (1.03)^{15} and multiply by 121.
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Final Result: This result is the GDP 15 years later given the annual growth rate.
Summary: To find GDP after 15 years with a specified growth rate, substitute the growth percentage into the formula and calculate to get the future GDP value. If you provide the growth rate, I can help calculate the exact number.