Question

The county debt is growing at an annual rate of 3.5%. What percent rate is it growing at per 2 years? Per 5
years? Per decade? Show the calculations that lead to each answer. Round each to the nearest tenth of a
percent.

Answer 1

Answer:

7.1225% per 2 years

18.77% per 5 years

41.06% per decade

Step-by-step explanation:

Suppose the the county debt is growing at an anual rate of x%.

After t years, the debt will be:

$D(t) = (1+x)^{t}$

In the formula, x goes as a decimal value.

In this problem, we have that:

Debt growing at a rate of 3.5% per year. So $x = 0.035$

Per 2 years

The debt after 2 years will be

$D(2) = (1+0.035)^{2} = 1.071225$

The initial debt is D(0) = 1.

So it will have grown 1.071225 - 1 = 0.071225 = 7.1225% per 2 years.

Per 5 years

The debt after 5 years will be

$D(2) = (1+0.035)^{5} = 1.1877$

The initial debt is D(0) = 1.

So it will have grown 1.1877 - 1 = 0.1877 = 18.77% per 5 years.

Per decade

The debt after 10 years will be

$D(2) = (1+0.035)^{10} = 1.4106$

The initial debt is D(0) = 1.

So it will have grown 1.4106 - 1 = 0.4106 = 41.06% per decade.