Question

1. Irene plans to save and invest annually, for the next 20 years, as follows:
Years 1-5: $3,500 per year
Years 6-7: $0 because she will take leave from work to get an MBA
Years 8-20: $5,000 per year
If she can earn 6% per year, and her contributions are made at the beginning of the years, how
much money will she have at the end of 20 years?

Answer 1

Let's look at the frequency of deposits made by Irene first at the beginning of the years.

A Year 1 2 Contribution 3500 3500 3500 3500 3500 9 10 12 5000 5000 5000 5000 5000 5000 5000 5000 5000 5000 5000 5000 5000 15 16 18 19 20

the amount of savings at Il we the have to calculate end of 20 years. the addition of The amount - Part of A savings will be & PartB I Part A will be the Future value of $3,500 deposited for first five years. We will use Future value of annuity formula to calculate the value at the end of 5th year. Then we will I compound the value @ 6% for remaining 15 years. Future value @ end of 5th years a px }(+)?1] x (1+>) n=5 Here P = $3500 8=6% Substituting the values 3500x [(1+0.00DX (1+0.00) 0.06 : 3500x ((1.338226-)x(100) 3500 X 0.06 0.35851911 0.06 3500X 5.9753185 20913.62 (rounded off ßom 20.913-615)

I Now, this 20913.615 will grow for another 15 years and at the end of 20 years, we will hare _ 20,913.615 (1+0.06% ( px (1 +234) where P = 20,913.615 r= 0.06 n = 15 We will have 20,913.615 (1.06 = 20,913.615 x 2.396558 = 50,120.695 - $50,120.70 Now, this amount is deposits Part A is done solely from those first 5 year Let's see whats in Part B where we deposit $5,000 from 8 - 20 years. same future value of annuity formula shall be used: px I ((1+r) 1) x (ltr)

n = 13 where P = $5000 r = 0.06 Now, substituting the values 5000x (1+0.06) – 3 x 0.00 5000 x 0.06 5000 X 5000x 17.1.062 1] x (1.06 0.06 5000x (2.132928-1) X1.06 0.06 1.132928X1.067 5000 x 0.06 5000 x 20.01506593 | $1000 75.33

Part B let's is also done. add part A answer. and Part B to arrive at the $50120.69 + $1000 75.33 $ 150, 196.02 Izene will have $150,196.02 in the end of 20 years.