Question

ou are planning to save for retirement over the next 30 years. To do this, you will invest $890 per month in a stock account and $490 per 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 return of 7.9 percent. How much can you withdraw each month from your account assuming a 25-year withdrawal period

Answer 1

Monthly withdraw= $23,294.99

Step-by-step explanation:

Giving the following information:

Stock:

Monthly deposit= $890

Number of periods= 30*12= 360

Interest rate= 0.109 / 12= 0.0091

Bond:

Monthly deposit= $490

Number of periods= 30*12= 360

Interest rate= 0.069 / 12= 0.00575

First, we need to calculate the amount of money collected at the moment of retirement. We need to use the following formula on each investment:

FV= {A*[(1+i)^n-1]}/i

A= monthly deposit

Stock:

FV= {890*[(1.0091^360) - 1]} / 0.0091

FV= $2,452,918.1

Bond:

FV= {490*[(1.00575^360) - 1]} / 0.00575

FV= $586,123.47

Total FV= 2,452,918.1 + 586,123.47

Total FV= $3,039,041.57

Now, the monthly withdrawal for 25 years:

Number of periods= 25*12= 300

Interest rate= 0.079 / 12= 0.0066

Monthly withdraw= (FV*i) / [1 - (1+i)^(-n)]

Monthly withdraw= (3,039,041.57*0.0066) / [1 - (1.0066^-300)]

Monthly withdraw= $23,294.99