Question

You are planning to save for retirement over the next 15 years. To do this, you will invest $1,100 a month in a stock account and $500 a month in a bond account. The return on the stock account is expected to be 7percent, and the bond account will pay 4 percent. When you retire, you will combine your money into an account with a 5 percent return. How much can you withdraw each month during retirement assuming a 20-year withdrawal period?

(A) $2,636.19
(B) $2,904.11
(C) $3,008.21
(D) $3,037.36
(E) $3,406.97

Answer 1

C $ 3,113.036

Step-by-step explanation:

First step will be calcualte the future value of the bond and stock funds:

`C * (1+r)^(time) -1)/(rate) = PV\\`

C 1,100

time 180 ( 15 years x 12 months)

rate 0.005833333 (7% divided into 12 months)

`1100 * ((1+0.00583333)^(180) -1 )/(0.00583333) = PV\\`

PV $348,658.5264

`C * ((1+r)^(time) -1)/(rate) = PV\\`

C 500

time 180

rate 0.003333 (4% divided by 12 months)

`500 * ((1+0.00333)^(180) -1)/(0.00333) = PV\\`

PV $123,045.2441

total fund: 348,658.5264 + 123,045.2441 = 471,703,7705

Then this will be placed to yield 5% and we will do motnly withdrawals:

we need to calcualte the PTM of this annuity:

`PV / (1-(1+r)^(-time) )/(rate) = C\\`

PV $471,703.77

time 240

rate 0.004166667

`471703.77 / (1-(1+0.00416667)^(-240))/(0.00416667) = C\\`

C $ 3,113.036