Beginning at age 35, Ms. Trinh invests $4000 each year into an IRA account until she retires. When she retires she plans to withdraw equal amounts each year that will deplete the account when she is 80. Find the annual amounts she will receive for each of the following retirement ages. Assume the account pays 5% compounded annually. (Round your final answers to two decimal places.)

I used the formula A = P(1+r/n)^nt

I solved the equation and got the following answers. Does anyone agree with me or can you show me what I did wrong.

I used the formula A = 4000[(1+0.05)^25-1]/0.05

(a) Retires at age 60.
$ 190908.40

I used the formula A = 4000[(1+0.05)^30-1]/0.05

(b) Retires at age 65.
$ 265755.39

I used the formula A = 4000[(1+0.05)^35-1]/0.05

(c) Retires at age 70.
$ 361281.23
------------------------

You quoted the wrong formula, but used the correct one in your calculations. Those give the future value, given her payments.

But the question is, what amount will she receive to deplete the funds at age 80? So, use the formula in reverse to find the PV=0 at age 80.

The amounts change dramatically, since earlier retirement provides less money, and there are more withdrawals by age 80.

To find the annual amounts Ms. Trinh will receive for each retirement age, we need to calculate the annuity payment. The annuity payment will be the amount that Ms. Trinh can withdraw each year from her IRA account in order to deplete it by the time she is 80.

The formula for calculating the annuity payment is as follows:
P = A * [(1 - (1 + r/n)^(-nt)) / (r/n)]
Where:
P = Principal or initial investment
A = Annuity payment (the amount Ms. Trinh will withdraw each year)
r = Annual interest rate (in decimal form)
n = Number of times the interest is compounded per year
t = Number of years

Let's calculate the annuity payments for each retirement age using the correct formula:

(a) Retires at age 60:
P = $4000 (annual investment)
r = 5% or 0.05
n = 1 (compounded annually)
t = 80 - 35 = 45 years (time period)

A = P * [(1 - (1 + r/n)^(-nt)) / (r/n)]
A = $4000 * [(1 - (1 + 0.05/1)^(-1*45)) / (0.05/1)]
A ≈ $14,307.69

Therefore, if Ms. Trinh retires at age 60, she will receive approximately $14,307.69 each year.

(b) Retires at age 65:
P = $4000 (annual investment)
r = 5% or 0.05
n = 1 (compounded annually)
t = 80 - 35 = 45 years (time period)

A = P * [(1 - (1 + r/n)^(-nt)) / (r/n)]
A = $4000 * [(1 - (1 + 0.05/1)^(-1*40)) / (0.05/1)]
A ≈ $9,347.25

Therefore, if Ms. Trinh retires at age 65, she will receive approximately $9,347.25 each year.

(c) Retires at age 70:
P = $4000 (annual investment)
r = 5% or 0.05
n = 1 (compounded annually)
t = 80 - 35 = 45 years (time period)

A = P * [(1 - (1 + r/n)^(-nt)) / (r/n)]
A = $4000 * [(1 - (1 + 0.05/1)^(-1*35)) / (0.05/1)]
A ≈ $5,850.96

Therefore, if Ms. Trinh retires at age 70, she will receive approximately $5,850.96 each year.

Based on the calculations using the correct formula and assumptions, the values you obtained using the formula A = 4000[(1+0.05)^nt-1]/0.05 are incorrect.