Chapter 16: Problem 12

Suppose a country has a real GDP equal to $\$ 1$ billion today. If this economy grows at a rate of 4 percent a year, what will be the value of real GDP after five years?

Short Answer

Expert verified

Answer: The value of the country's real GDP after five years will be approximately \$1.22 billion.

Step by step solution

Identify the given values

In this problem, we are given the following information: - Real GDP today: $\$1$ billion - Annual growth rate: $4\%$ - Time: $5$ years

Convert the percentage growth rate to a decimal

We need to convert the given growth rate (4%) to a decimal form. To do this, divide the percentage by 100: $4\% = \dfrac{4}{100} = 0.04$

Apply the compound interest formula

We will apply the compound interest formula to determine the value of real GDP after five years: $Future\ Real\ GDP = Present\ Real\ GDP\ (1 + Annual\ Growth\ Rate)^{Time}$

Plug in the given values and calculate

Now we will plug in the given values into the formula: $Future\ Real\ GDP = \$1\ billion\ (1 + 0.04)^{5}$ Calculate the value inside the parentheses first: $(1 + 0.04) = 1.04$ Then raise this result to the power of 5: $(1.04)^{5} = 1.2166529$ Finally, multiply this result by the present real GDP ($"1$ billion): $Future\ Real\ GDP = \$1\ billion \times 1.2166529 = \$1.2166529\ billion$

Round the result and interpret

We will round the result to two decimal places: $Future\ Real\ GDP = \$1.22\ billion$ After five years of growing at a $4\%$ annual growth rate, the value of the real GDP in this country will be approximately $\$1.22$ billion.