Question

If we were able to invest a Gradient = $100 at the end of each year for 7 years at 6% interest (i.e., So at the end of year 1, $100 at the end of year 2, $200 at the end of year 3, ..., and $600 at the end of year 7), what Annual amount or Annuity could we take out of the bank starting at the end of the first year and continuing until the end of the seventh year?

Answer 1

We can withdraw an equivalent annuity of $ 293.658 each year.

Step-by-step explanation:

We build a scheduled table to know the future value of the gradient investment

Time Beg Gradient Total Rate Ending

1 $100.00 $100.00 $100.00 0.060 $106.00

2 $106.00 $100.00 $206.00 0.060 $218.36

3 $218.36 $200.00 $418.36 0.060 $443.46

4 $443.46 $300.00 $743.46 0.060 $788.07

5 $788.07 $400.00 $1,188.07 0.060 $1,259.36

6 $1,259.36 $500.00 $1,759.36 0.060 $1,864.92

7 $1,864.92 $600.00 $2,464.92 0.060 $2,612.81

Then, we solve for the equivalent annuity-due:

`PV / (1-(1+r)^(-time) )/(rate)(1+rate) = C\\`

PV 2,613

time 7

rate 0.06

`2612.81 / (1-(1+0.06)^(-7) )/(0.06)(1+0.06) = C\\`

C $ 293.658

Itis annuity due as we will going to retire cash in a 6 year period for seven times. (at each year-end during 6 years thus, annuity-due

1st 2nd 3rd 4th 5th 6th 7th

/-------/-------/-------/-------/-------/-------/-------/

1 2 3 4 5 6 7