Question

Suppose Rachel wants to withdraw $2,775 each month for 20 years. how much does she have to invest (present value) in an annuity that has an annual interest rate of 6%? round your answer to the nearest hundred.

Answer 1

Rachel needs to invest approximately $392,400 in an annuity with an interest rate of 6% in order to withdraw $2,775 each month for 20 years.

Step-by-step explanation:

To find the amount Rachel needs to invest (present value) in an annuity, we can use the present value formula for an ordinary annuity:

PV = PMT * ((1 - (1 + r)^(-n)) / r)

Where PV is the present value, PMT is the monthly withdrawal amount, r is the annual interest rate divided by 12 (since we're calculating monthly withdrawals), and n is the total number of months (20 years * 12 months/year).

Plugging in the values from the question, we have:

PV = 2775 * ((1 - (1 + 0.06/12)^(-20*12)) / (0.06/12))

Simplifying this expression gives us:

PV ≈ $392,408.45

Therefore, Rachel needs to invest approximately $392,400 to be able to withdraw $2,775 each month for 20 years.

Answer 2

Rachel's initial investment requirement to withdraw $2,775 monthly for 20 years from an annuity with a 6% annual interest rate is calculated using the present value of an annuity formula and rounded to the nearest hundred.

Step-by-step explanation:

The question asks how much Rachel needs to invest today to be able to withdraw $2,775 each month for 20 years from an annuity with a 6% annual interest rate. To calculate this, we need to determine the present value (PV) of the annuity. The formula for finding the present value of an annuity is PV = PMT × [(1 - (1 + r)-n) / r], where PMT is the monthly withdrawal amount, r is the monthly interest rate, and n is the total number of withdrawals.

Rachel plans to make withdrawals for 20 years, which corresponds to 240 months (20 years × 12 months). The annual interest rate is 6%, so the monthly interest rate would be 0.06 / 12 = 0.005. Substituting these values into the formula, we would calculate Rachel's initial investment requirement. Since this question requires rounding to the nearest hundred, the final PV value would also be rounded accordingly.