Question

You are planning your retirement in 10 years. You currently have $171,000 in a bond account and $611,000 in a stock account. You plan to add $6,900 per year at the end of each of the next 10 years to your bond account. The stock account will earn a return of 11.25 percent and the bond account will earn a return of 7.75 percent. When you retire, you plan to withdraw an equal amount for each of the next 24 years at the end of each year and have nothing left. Additionally, when you retire you will transfer your money to an account that earns 7 percent.How much can you withdraw each year in your retirement?

Answer 1

$194,767.71

Explanation :

As per the data given in the question,

Future value of ordinary annuity = C × [(1+i)^n - 1 ÷ i]

value of bond = $171,000 × (1+0.0775)^10 + $6,900 × ((1+0.0775)^10 - 1) ÷ 0.0775

= $360,718.90 + $98,778.37

= $459,497.27

Now

Future value of stock = $6,11000 × (1+0.1125)^10

= $1,774,358.645

Combined value = $459,497.27 + $1,774,358.645

= $2,233,855.92

After solving this, we need to apply the PMT formula for yearly payment i.e to be shown below

NPER = 24 years

RATE = 7%

PV = $2,233,855.92

FV= 0

The formula is shown below:

= PMT(RATE;NPER;-PV;FV;0)

The present value comes in negative

After applying the above formula, the yearly payment is $194,767.71