Question

You are planning your retirement and you come to the conclusion that you need to have saved $1,250,000 in 30 years. You can invest into a retirement account that with earn you a 5% average annual return.

Required:

i.            If your investment can earn 5% annually, how much would you need to put into your account at the end of each year to reach your retirement goal?

ii.            If your investment can earn 10% annually, how much would you need to put into your account at the end of each year to reach your retirement goal?

iii.           With regard to retirement and your answers above (i, ii), discuss the importance of earning a higher return on your investments?

Answer 1

This is an annuity problem;

Future value of annuity= A*[(1+r)^n-1]/r

where A=annuity payment per year; r=interest rate ; n=no of years

i: @ 5% interest

1250000=A*[(1+5%)^30 -1]/.05

A=18814.29

ii: @ 10% interest

1250000=A*[(1+10%)^30 -1]/.1

A=7599.06

iii:

As you can see with a higher return of 10% the per year deposit needed to reach a particular amount has significantly reduced. Hence it is important for us to get a higher return for our money which can help the money grow cumulatively.