Answer to Question #248089 in Finance for Silva

Question

2. Sam (20 years old) and Peya (30 years old), starts to work at UNAM today. Sam invests N$ 2500 per month and Peya invest N$ 3500 per month in a retirement fund. Suppose both have to retire at the age of 65, and assume the fund give returns of 9% per annun, compound monthly. (a) Find the value of their investment when they retire. [6] (b) If Peya is to accumulate the same amount as Sam on the retirement date, how much should Peya contribute per month to the fund to achieve that?. [3] (c) Peya decide to invest N$ 4500 per month in the fund. At what age Peya will accumulate the same amount as Sam? [3] (d) Suppose Sam invest N$ 3000 per month only for the first ten years and to leave the final amount in the fund for the remaining years until his retirement. Find his final value of retirement when he retires.

Answer 1

a) A= Monthly deposit , i = Interest rate, n = no of years

Value of Asset = A ($\frac{(1+ i )^n{-1}}{i}$ )

Sam

A= $2500, i = 0.075 (9%/12), n = 540 ((65-20)*12=45*12)

=$2500 (1.0075)^540 - 1 / 0.0075

=$2500 x 7404.878469

= $18512,196.17

Peya

A= $3000, i = 0.075 (9%/12), n = 420 ((65-30)*12=35*12)

=$3000 (1.0075)^420 -1/.0075

=$3000 x 2941.784474

= $8825,353.42

b) $6,292.85

$\frac {Required \; amount}{FV \; annuity \; factory} = \frac {18512,196.17}{2941.784474} =6,292.85$

c) Age = 68.60

=$1,85,12,196.17 = $4500 ((1.0075)^540 - 1) / 0.0075

=(4113.821371 x 0.0075)+1 = (1.0075)^n

=38.60

= 30+38.60 = 68.60

d) Total = $580,542.83 + $13389,281.99 = $13969,824.82

Amount for 10 years

$3000 (1.0075)^120 - 1 / 0.0075

= 193.51 x 3000 = $580,542.83

Remaining Interest

$483785.69 (1.0075)^(35*12) = $13389,281.99