Question

Find the time required for an investment of 5000 dollars to grow to 6000 dollars at an interest rate of 7.5 percent per year, compounded quarterly.

Your answer is t=

Answer 1

To find the time required for an investment to grow to a certain amount with compound interest, we can use the formula Final Balance = Principal(1 + interest rate/number of compounding periods)^(number of compounding periods * time). In this case, the investment of $5000 will take approximately 4.08 years to grow to $6000 at an interest rate of 7.5% per year, compounded quarterly.

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 Balance = Principal(1 + interest rate/number of compounding periods)^(number of compounding periods * time)

In this case, the initial principal is $5000, the final balance is $6000, the interest rate is 7.5% (or 0.075), and the interest is compounded quarterly (so there are 4 compounding periods per year).

1. Convert the interest rate to a decimal: 0.075
2. Substitute the known values into the formula: 6000 = 5000(1 + 0.075/4)^(4*time)
3. Divide both sides by 5000: 1.2 = (1 + 0.075/4)^(4*time)
4. Take the natural logarithm of both sides: ln(1.2) = ln((1 + 0.075/4)^(4*time))
5. Divide both sides by ln((1 + 0.075/4)^(4*time)): time = ln(1.2)/ln((1 + 0.075/4)^(4*time))

Using a calculator, we can solve for time to find that the investment will take approximately 4.08 years to grow from $5000 to $6000.