The Compound Interest Calculation for an Investment of $710 Growing to $1,000 at a 3.5% Annual Compound Interest Rate

D

If it takes n years for the growth, then 1000 = 710*(1+3.5%)^n. Solving for n gives 9.96 years.

To solve this problem, we can use the formula for compound interest:

Future Value = Present Value * (1 + Interest Rate)^Number of Periods

In this case, the Present Value (PV) is $710, the Future Value (FV) is $1,000, and the Interest Rate is 3.5% or 0.035. We need to find the Number of Periods.

Plugging in the given values into the formula, we have:

$1,000 = $710 * (1 + 0.035)^Number of Periods

Now, let's solve for the Number of Periods:

(1 + 0.035)^Number of Periods = $1,000 / $710

Dividing both sides by $710, we get:

(1 + 0.035)^Number of Periods = 1.4085

To isolate the exponent, we take the natural logarithm (ln) of both sides:

ln[(1 + 0.035)^Number of Periods] = ln(1.4085)

Using the property of logarithms that ln(a^b) = b * ln(a), we have:

Number of Periods * ln(1 + 0.035) = ln(1.4085)

Now, we can solve for the Number of Periods:

Number of Periods = ln(1.4085) / ln(1 + 0.035)

Using a calculator or a mathematical software, we find:

Number of Periods ≈ 9.042

Since the Number of Periods represents the number of years, we round up to the nearest whole number. Therefore, it would take approximately 9 years for the investment of $710 to grow to $1,000.

Therefore, the correct answer is A. 9 years.