How Long to Double Your Investment?

How long does it take for $14,050 to grow to $26,500, if interest rates are set at 15%?

A. 4.54 years

B. 423.33 years

C. 0.59 years

D. 12.23 years

Answer:

It will take approximately 12.23 years for the initial investment of $14,050 to grow to $26,500 at an interest rate of 15%.

To calculate the time it takes for an investment to grow from an initial value to a future value, we can use the concept of compound interest. Compound interest takes into account the accumulation of interest on both the initial amount and any interest that has been earned over time.

In this case, we have an initial investment of $14,050 and a future value of $26,500. The interest rate is set at 15%. We want to determine the time it takes for the investment to grow to the future value.

Using the formula for compound interest:

FV = PV x (1 + r)^n

We can rearrange the formula to solve for time:

Time = log(Future Value / Present Value) / log(1 + Interest Rate)

Plugging in the given values:

Time = log(26,500 / 14,050) / log(1 + 0.15) ≈ 12.23 years

Therefore, it will take approximately 12.23 years for the initial investment of $14,050 to grow to $26,500 at an interest rate of 15%. This means that if the investment continues to earn a 15% interest rate, it will take approximately 12.23 years to double the initial investment.