Question

You want $1,000,000 when you retire in 40 years. You decided to save some money every year next 40 years for your retirement. You are going to open Roth IRA and invest everything in Vanguard S&P 500 Funds that expect to earn 6 percent annually. If your contribution starts a year from today, how much must you contribute every year next 40 years? Round to the nearest cent. Do not include any unit (If your answer is $111.11, then type 111.11 without $ sign.)
You are starting your new career today after graduating. You decided to contribute $500 a month into a fund that is expected to earn 6 percent, compounded monthly. If you start the contribution a month from today for 30 years, how much will you have right after you contribute the last $500 in 30 years? Round to the nearest cent. Do not include any unit (If your answer is $111.11, then type 111.11 without $ sign.)

Answer 1

Answer:

Instructions are listed below.

Explanation:

Giving the following information:

A) You want $1,000,000 when you retire in 40 years. It earns 6 percent annually.

We need to use the following version of the final value formula:

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

A= annual deposit

Isolating A:

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

FV= 1,000,000

n=40

i=0.06

A= (1,000,000*0.06) / [(1.06^40)-1]

A= $6,461.53

B) You decided to contribute $500 a month into a fund that is expected to earn 6 percent, compounded monthly. If you start the contribution a month from today for 30 years.

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

A= annual deposit

n= 30*12= 360

i= 0.06/12= 0.005

A= 500

FV= {500*[(1.005^360)-1]}/0.005= $502,257.52