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

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TomShelby TomShelby · Answer 1 · 2019-10-03T02:35:09+02:00

Answer:

C $ 3,113.036

Explanation:

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

[tex]C \times \frac{1+r)^{time} -1}{rate} = PV\\[/tex]

C 1,100

time 180 ( 15 years x 12 months)

rate 0.005833333 (7% divided into 12 months)

[tex]1100 \times \frac{(1+0.00583333)^{180} -1 }{0.00583333} = PV\\[/tex]

PV $348,658.5264

[tex]C \times \frac{(1+r)^{time} -1}{rate} = PV\\[/tex]

C 500

time 180

rate 0.003333 (4% divided by 12 months)

[tex]500 \times \frac{(1+0.00333)^{180} -1}{0.00333} = PV\\[/tex]

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:

[tex]PV \div \frac{1-(1+r)^{-time} }{rate} = C\\[/tex]

PV $471,703.77

time 240

rate 0.004166667

[tex]471703.77 \div \frac{1-(1+0.00416667)^{-240}}{0.00416667} = C\\[/tex]

C $ 3,113.036