Question

If you deposit $10000 each year for 10 years starting 3 years from now, how much equal amounts of money will have to be withdrawn 20 and 25 years from now in order to deplete the account? Use an interest rate of 10% per year.

Answer 1

Ans. =

Annuity = 10000
N = 10
Interest Rate = 10%

Future Value at t=10:
= [(1+r)^N - 1] / r
= [(1.10)^10 - 1] / .10
= $159374

Future Value at t=20:
= Present Value × (1+r)^N
= 159374 × (1.10)^10
= $413375

Annuity from 20 to 25 Years:

N = 5
Interest Rate = 10%
Present Value at t=20 = $413375

Present Value = Annuity × (1- 1/(1+r)^N)/r

413375 = Annuity × (1- 1/(1.10)^5) 0.10

Annuity for time 20 to 25 years = $109047.48

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