Question

Ramesh wants to accumulate Rs. 1000000 in the next 25 Years to retire comfortably. Assuming he is able to
get a rate of return of 9% on his investment, what is the annual savings he needs to set aside at the
beginning of each year to achieve this goal?
10331
10831
11331
11831-
​

Answer 1

Given : Ramesh wants to accumulate Rs. 1000000 in the next 25 Years to retire comfortably. Assuming he is able to  get a rate of return of 9% on his investment,

To find : annual savings he needs to set aside at the  beginning of each year to achieve this goal?

Solution:

Saving each Year  =   S

saving in 25 Years  = 25S

Using SI

Interest earned for saving 1st year is for 25 Years

For next year  for 24 Years

SI = P * R * T /100

Interest =  (S * 9 / 100)(25 + 24 + ...........................+ 1)

= (9S/100)(25 * 13)

= 117S/4

25S + 117S/4  =1000000

=> 217S =  4000000

=> S = 18,433  

None of the given option matches.

Using compound interest

Amount of 1st year deposit =  S( 1 + 9/100)²⁵

Amount of 2nd year deposit =  S( 1 + 9/100)²⁴

and so on

S( 1 + 9/100)²⁵ + S( 1 + 9/100)²⁴ +............................+  S( 1 + 9/100)¹

=  S( 1 + 9/100)¹ + ...........................+ S( 1 + 9/100)²⁴ + S( 1 + 9/100)²⁵

a = S( 1 + 9/100) = S(1.09)

r = ( 1 + 9/100) = 1.09

n = 25

= S(1.09) ( 1.09²⁵ - 1 )/(1.09 - 1)  = 1000000

=> S ( 1.09²⁵ - 1 ) = 82,568.81

=> S = 10,831.4

10831 is close

10831 is the annual savings he needs to set aside at the  beginning of each year to achieve this goal

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