Question

Jan is 62 and is considering retiring soon. She has $680,000 in a fund paying interest at an annual rate of 4.2% compounded continuously. She would like to withdraw a fixed amount continuously after she retires, and have a balance of $80,000 when she is 90 years old. Assume a continuous money flow, then she can spend $ _______ each month. (Round the answer to an integer at the last step.)

Answer 1

She can spend $ 3,323 each month

Step-by-step explanation:

Jan's current age = 62 years, Retirement age = 90 years, n = 90 - 62 = 28 years

The total amount of balance she should have at 90 years = $80,000

PV is Present Value

PV of this amount = 80,000 x e-r x n = 80,000 x e-4.2% x 28 = 24,680.83

PV of amount available for withdrawal = 680,000 - 24,680.83 = $ 655,319.17

Effective monthly rate, rm = er x 1/12 - 1 = e4.2% x 1/12 - 1 = 0.3506%

If Q is the amount she can spend each month till 28 years i.e. 28 x 12 = 336 months, then PV of Q as annuity = $ 655,319.17

Q / rm x [1 - (1 + rm)-336] = Q / 0.3506% x [1 - (1 + 0.3506%)-336] = 655,319.17

Q x 197.2229383 = 655,319.17

Q = 3,322.73

Therefore, she can spend $ 3,322.73 each month