Question

Steven wishes to save for his retirement by depositing $2,000 at the beginning of each year for thirty years. Exactly one year after his last deposit, he wishes to begin making annual level withdrawals until he has made twenty withdrawals and used up the savings. Find the amount of each withdrawal if the effective interest rate is 3% during the first thirty years but only 2% after that.

Answer 1

Explanation:

i = interest 3% for 30 years

This is a simple dynamical system for whom the the solutions are given as

`S=R[((i+1)^n-1)/(i)](i+1)`

putting values we get

S=2000[\frac{(1.03)^{30}-1}{0.03}](1.03)

= $98005.35

withdrawal of money takes place from one year after last payment

To determine the result we use the present value formula of an annuity date

`P = R(1-(1+i)^(-n))/(i){i+1}`

we need to calculate R so putting the values and solving for R we get

R= $6542.2356