Question

You’ve got the best idea for a new business but you need to get some mentoring skills and need to save some money before you launch. You plan to save $6,800 every year for the first 4 years (t=1 through t=4) and then you expect you will be able to save $12,000 in the following four years (t=5 through t= 8). That first deposit will be made one year from today. You caught a break and won $30,000 in the lottery yesterday so you immediately deposited it. You are expecting the stock market to earn at least 5% compounded annually over the entire period. How much will you have to start your new business in 8 years from now? (Show how you got this answer )

Answer 1

Total amount at the end of 8 years

compounded value of $ 30000 deposited for 8 years compounded annually at 5% +

Compounded value of $6800 for eight years compounded annually at 5% +

Compounded value of $5200 for 4 years compounded annually at 5%

total amount = (30000*1.477) + (6800*9.549) + (5200* 4.310)

= 44310 + 64933.2 + 22412

= 129655.20

So total compounded value at the end of entire eight years will be 129655.20

1.477 is compound factor at interest rate 5% for 8 years

9.549 is compound factor for annuity at rate 5% for 8 years

4.310 is compound factor for annuity at rate 5% for 4 years

6800 has been invested for all the eight years and 5200 (12000-6800) has been invested annually for four years.