Question

9)As part of you financial planning and to supplement your retirement, you decided to save $3,000 at the end of each year for 30 years, how much money you will have in your account if you can earn 10% ?

10) Referring to question number 9, Assume that you deposited the money at the beginning of the year, how much money you would find in your account in the 30 years?

*need steps**

Answer 1

9)

The stream of cash flows represents an annuity

We need to calculate the future value of annuity

Future value of annuity

= P x [ ( 1 + r ) ^ n – 1] / r

Where,

P = Annual payments at the end of the year = $3,000

r = Rate of interest = 10% or 0.10

n = Number of years = 30

So, Future value of annuity

= $3,000 x [ 1.10 ^ 30 – 1 ] / 0.10

= $3,000 x [17.449402 – 1 ] / 0.10

= $3,000 x 164.494022

= $ 493,482.07

10)

The stream of cash flows represents annuity due

Future value of annuity due

= ( 1 + r ) x P x [ ( 1 + r ) ^ n – 1] / r

= 1.10 x $3,000 x [ 1.10 ^ 30 – 1 ] / 0.10

= 1.10 x $3,000 x [17.449402 – 1 ] / 0.10

= 1.10 x $3,000 x 164.494022

= 1.10 x $ 493,482.07

= $542,830.27