Question

Find the time (in yr) required for an investment of $4,000 to grow to $8,000 at an interest rate of 7.5% per year, compounded quarterly. (round your answer to two decimal places.)

Answer 1

To find the time required for an investment of $4,000 to grow to $8,000 at an interest rate of 7.5% per year, compounded quarterly, we can use the compound interest formula. Plugging in the values and solving for Time gives us approximately 9.47 years.

Step-by-step explanation:

To find the time required for an investment to grow to a certain amount with compound interest, we can use the formula:

Final Amount = Principal * (1 + Interest Rate / Number of periods)^(Number of periods * Time)

In this case, the Principal is $4,000, the Final Amount is $8,000, the Interest Rate is 7.5% per year, compounded quarterly. Let's plug in these values and solve for Time:

$8,000 = $4,000 * (1 + 0.075 / 4)^(4 * Time)

Dividing both sides of the equation by $4,000, we get:

2 = (1 + 0.075 / 4)^(4 * Time)

Take the natural logarithm of both sides to solve for Time:

ln(2) = 4 * Time * ln(1 + 0.075 / 4)

Divide both sides by 4 * ln(1 + 0.075 / 4):

Time ≈ ln(2) / (4 * ln(1 + 0.075 / 4))

Using a calculator, we can find that Time ≈ 9.47 years (rounded to 2 decimal places).