Question

1. You are trying to plan for retirement in 20 years and currently you have $50,000 in a savings account and $80,000 in stocks. In addition, you plan to add to your savings by depositing $10,000 per year in your savings account at the end of each of the next 20 years, until retirement. Assume that your savings account returns 5% compounded annually and your investment in stocks will return 10% compounded annually, how much do you have at the end of 20 years? (Ignore taxes)

Answer 1

I have $ 50000 is my saving account so After 20 year, I will have

Future value = PV x (1+r)ⁿ

Where n is number of year which is 20 and r is rate of interest 5%

FV = 50000 x (1.05)²⁰

=$ 132664.89

Now I also deposite $10000 every year which is a case of future Annuity, after 20 year I have

Fv = deposite x {[(1+r)²⁰ -1]/ r }

= $10000 X {[(1.05)²⁰ -1]/ 0.05

= 10000 x 1.65/0.05

= 10000 x 33

= $ 330000

So after 20 year I will have $330000 + $132664.89

= $462664.89 in my saving acount

Now I make an investment of $ 80000 at 10% rate of interest for 20 year

Fv of stock = 80000 x (1.1)²⁰

= $ 538200

At the end of 20 year I will have

= $ 462664.89 + $ 538200

= $ 1000864.89