Question

30. Kendra wants to be able to make withdrawals of $60,000 a year for 30 years after retiring in 35 years. How much will she have to save each year up until retirement if her account earns 7% interest

Answer 1

Answer:

Annual deposit= $5,386

Explanation:

First, we need to calculate the capital required when she retires. We will use the following formulas:

FV= {A*[(1+i)^n-1]}/i

A= annual withdraw

FV= {60,000*[(1.07^30) - 1]} / 0.07

FV= $5,667,647.18

PV= FV/(1+i)^n

PV= 5,667,647.18/1.07^30

PV= $744,542.47

At retirement, she needs $744,542.47

Now, we can determine the annual deposit:

FV= {A*[(1+i)^n-1]}/i

A= annual deposit

Isolating A:

A= (FV*i)/{[(1+i)^n]-1}

A= (744,542.47*0.07) / [(1.07^35) - 1]

A= $5,386