Amy invested $500 per month in a 401k that earned 6% annual return for 40 years. Hank invested $1,000 per month in a 401k that also earned 6% annual return, but for 20 years. Which of the following would be true?

The correct option is a. Amy’s balance would be greater than Hank’s in the end.

Step-by-step explanation:

Note: This question is not complete. The complete question is therefore provided before answering the question as follows:

Amy invested $500 per month in a 401k that earned 6% annual return for 40 years. Hank invested $1,000 per month in a 401k that also earned 6% annual return, but for 20 years. Which of the following would be true?

a. Amy’s balance would be greater than Hank’s in the end.

b. Amy’s balance is $5,142 and Hank’s balance is $3,207.

c. Hank’s balance would be greater than Amy’s in the end.

d. The investment and balance would be the same.

e. None of these are true

The explanation to the answer is now given as follows:

The balance in the end for each can be determined using the formula for calculating the Future Value (FV) of an Ordinary Annuity as follows:

FV = M * (((1 + r)^n - 1) / r) (1)

Where;

For Amy:

FV = Future value or balance in the end = ?

M = Monthly investment = $500

r = Monthly interest rate = 6% / 12 = 0.06 / 12 = 0.005

n = number of months the investment will be made = 40 years * 12 months = 480

Substituting the values into equation (1), we have:

FV = $500 * (((1 + 0.005)^480 - 1) / 0.005)

FV = $500 * 1,991.49

FV = $995,745.37

Therefore, Amy’s balance would be $995,745.37 in the end.

For Hank:

FV = Future value or balance in the end = ?

M = Monthly investment = $1,000

r = Monthly interest rate = 6% / 12 = 0.06 / 12 = 0.005

n = number of months the investment will be made = 20 years * 12 months = 240

Substituting the values into equation (1), we have:

FV = $1,000 * (((1 + 0.005)^240 - 1) / 0.005)

FV = $1,000 * 462.04

FV = $462,040.90

Therefore, Hank’s balance would be $462,040.90 in the end.

Conclusion

Since Amy’s balance of $995,745.37 is greater than Hank’s balance $462,040.90, it therefore implies that the correct option is a. Amy’s balance would be greater than Hank’s in the end.

The equation is  

The value of x is 28 cookies

Step-by-step explanation:

Let

x ---->  the number of cookies she baked last week

we know that

The number of cookies she baked last week multiplied by 3 minus 4 must be equal to 80 cookies

so

The linear equation that represent this situation is

solve for x