Question

Jade and his twin sister Laura are both 20 years old. They have both decided to save for their retirement. Jade will invest $500 per year (end of the year) for the coming 10 years. Then he will stop investing but will keep the money in the bank till the age of 65. Laura on the other hand will start investing $500 per year (end of the year) 10 years from now and until her retirement (age of 65).

Assuming a flat rate of 10% per annum, who will have more money at the time of their retirement.

Answer 1

JADE WILL HAVE MORE MONEY , mONEY WITH JADE AT THE AGE OF 65 = $223940.2

AND MONEY WITH LAURA = $135512.2, JADE WILL HAVE $223940.2- $135512.2 = $88428 MORE MONEY, EXPLANATION IS GIVEN BELOW

Jade invests $500 at the end of the year for 10 years , rate of interest = 10% , after 10 years amount will be kept for 65-30 = 35 years ...( 65 = Age od Jade when retires, 30 = 10 years from now, 20+10).

FUTURE VALUE AT THE END OF TENTH YEAR = PV + PV(1+R) +PV(1+R)^2 + PV(1+R)^3+........PV(1+R)^9

THEN AFTER THAT PUT THAT MONEY FOR 35 YEARS ,FINAL VALUE IS THEN CALCULATED AS PV(1+R)^35

FV AT THE END OF 10 YEARS = 500 + 500(1+0.1) + 500(1.01)^2 + 500(1.01)^3+....500(1.1)^9

=

500

+ 550

+ 605

+ 665.5

+ 732.05

+ 805.255

+ 885.7805

+ 974.3586

+ 1071.794

+ 1178.974

AT THE END OF 10 years , amount will become sum of these values that is $7968.71

This $7968.71 will be kept for another 35 years at 10 Percent interest = final value = PV(1+R)^t ,

PV = 7968.71 , r= 10%, T= 35 , SUBSTITUTING THE VALUES IN THE FORMULA

7968.71(1+.1)^35 = $223940.2

B) LAURA INVETS $500 FOR 35 YEARS , THEREFORE FINAL VALUE =

SUM OF PV + PV(1+R) +PV(1+R)^2 + PV(1+R)^3+........PV(1+R)^35 =

500 + 500(1+0.1) + 500(1.01)^2 + 500(1.01)^3+....500(1.1)^35 =  

SUM OF

500

550

605

665.5

732.05

805.255

885.7805

974.3586

1071.794

1178.974

1296.871

1426.558

1569.214

1726.136

1898.749

2088.624

2297.486

2527.235

2779.959

3057.955

3363.75

3700.125

4070.137

4477.151

4924.866

5417.353

5959.088

6554.997

7210.497

7931.546

8724.701

9597.171

10556.89

11612.58

12773.83

= $135512.2,