You are planning to save for retirement over the next 30 years. To do this, you will invest $890 a month in a stock account and $490 a month in a bond account. The return of the stock account is expected to be 10.9 percent, and the bond account will pay 6.9 percent. When you retire, you will combine your money into an account with a 7.9 percent return.

You are planning to save for retirement over the next 30 years. To do this, you will invest $890 a month in a stock account and $490 a month in a bond account. The return of the stock account is expected to be 10.9 percent, and the bond account will pay 6.9 percent. When you retire, you will combine your money into an account with a 7.9 percent return.

How much can you withdraw each month from your account assuming a 25-year withdrawal period? (Do not round intermediate calculations and round your final answer to 2 decimal places. (e.g., 32.16))

Withdrawal

$ per month

Explanation:

We need to find the annuity payment in retirement. Our retirement savings ends and the retirement withdrawals begin, so the PV of the retirement withdrawals will be the FV of the retirement savings. So, we find the FV of the stock account and the FV of the bond account and add the two FVs.

Stock account: FVA = $890[{[1 + (0.109/12)]360 − 1} / (0.109/12)] = $2,442,269.68

Bond account: FVA = $490[{[1 + (0.069/12)]360 − 1} / (0.069/12)] = $586,123.47

So, the total amount saved at retirement is:

$2,442,269.68 + 586,123.47 = $3,028,393.15

Solving for the withdrawal amount in retirement using the PVA equation gives us:

PVA = $3,028,393.15 = $C[1 – {1 / [1 + (0.079/12)]300} / (0.079/12)]

C = $3,028,393.15 / 130.68420 = $23,173.37 withdrawal per month

   

Calculator Solution:

Note: Intermediate answers are shown below as rounded, but the full answer was used to complete the calculation.

Stock account:

 

Enter

360

10.9% / 12

$890

N

I/Y

PV

PMT

FV

Solve for

$2,442,269.68

 

Bond account:

 

Enter

360

6.9% / 12

$490

N

I/Y

PV

PMT

FV

Solve for

$586,123.47