To calculate the future value of an investment compounded quarterly, you can use the formula:

FV = P * (1 + r/n)^(nt)

where:
- FV is the future value of the investment
- P is the principal amount (the initial amount of money)
- r is the annual interest rate (in decimal form)
- n is the number of times that interest is compounded per year
- t is the time the money is invested for in years

Given in the problem:
P = $5000
r = 7% or 0.07
n = 4 (since it's compounded quarterly)
t = 3 years

Substitute these values into the formula:

FV = 5000 * (1 + 0.07/4)^(4*3)

Calculate the value inside the parentheses first:

1 + 0.07/4 = 1.0175

Then raise this to the power of 4*3 = 12:

(1.0175)^12 = 1.230769

Finally, multiply this by the principal amount:

5000 * 1.230769 = $6144.57

So, the future value of $5000 invested at a 7% interest rate compounded quarterly for 3 years is $6144.57. Therefore, the correct answer is a) $6144.57.

Question

To calculate the future value of an investment compounded quarterly, you can use the formula:

FV = P * (1 + r/n)^(nt)

where:
- FV is the future value of the investment
- P is the principal amount (the initial amount of money)
- r is the annual interest rate (in decimal form)
- n is the number of times that interest is compounded per year
- t is the time the money is invested for in years

Given in the problem:
P = $5000
r = 7% or 0.07
n = 4 (since it's compounded quarterly)
t = 3 years

Substitute these values into the formula:

FV = 5000 * (1 + 0.07/4)^(4*3)

Calculate the value inside the parentheses first:

1 + 0.07/4 = 1.0175

Then raise this to the power of 4*3 = 12:

(1.0175)^12 = 1.230769

Finally, multiply this by the principal amount:

5000 * 1.230769 = $6144.57

So, the future value of $5000 invested at a 7% interest rate compounded quarterly for 3 years is $6144.57. Therefore, the correct answer is a) $6144.57.

Knowee AI · Accepted Answer