Question

By the end of this year you would be 35 years old and you want to plan for your retirement. You wish to retire at the age of 65 and you expect to live 20 years (I hope more) after retirement. Upon retirement you wish to have an annual sum of $50,000 to supplement your social security benefits. A conservative bond fund has been returning 7% annually and you decide to invest your retirement money in this fund. Assuming that the fund continues to return at least 7% during your planning horizon before and after retirement, how much should you invest in the fund starting from now, annually, in order to be able to withdraw $50,000 per year during your retirement?

Answer 1

$10586.40

Step-by-step explanation:

50,000*20= $1,000,000

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

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

A= (1000000*0.07)/[(1.07^30)-1]

A=$10586.40

Answer 2

The annual payments are= $10586.40

Step-by-step explanation:

Giving the following information:

By the end of this year, you would be 35 years old and you want to plan for your retirement.

You wish to retire at the age of 65 and you expect to live 20 years more.

You wish to have an annual sum of $50,000.

A conservative bond fund has been returning 7% annually.

First, we need to calculate the amount of money needed at 65 years old.

50000*20= $1,000,000

So, we know the final value= 1,000,000; n=30 and the interest rate i=0.07

We need to find the annual payments required to achieve the final value, using the following formula:

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

A= annual payment

Isolating A:

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

A= (1000000*0.07)/[(1.07^30)-1]

A=$10586.40