Question

 man stipulate his will?

that Rs 50,000 from his estates is to be place in fund from which his three daughters are each to receive the same amount when aged 21 . when the man dies, the girls are aged 19, 15 and 13 years . how much will each receive, if the funds earns interest 12% compounded semi-annually .​

Answer 1

Rs 50000 to be distributed among Daughters ages 19 , 15 & 13 Each so that Each Daughter will Receive  Equal amount at age of 21 = Rs 29714

Step-by-step explanation:

Total Fund = 50000

Rate of interest = 12 % per annum compounded semi annually

=> 6%  Semi Annually

Aged 19 will get 2 Year = 4 * 6 months interest

Aged 15 will get 6 Years = 12 * 6 months interest

Aged 13 will get 8 years = 16 * 6 months interest

Let say Each will Get X

Amount after 2 Years = 50000 * ( 1 + 6/100)⁴ - X  ( as 19 year will get her Amount)

= 50000 * ( 1.06)⁴ - X

Amount after 6 Years ( 4 Years more) = (50000 * ( 1.06)⁴ - X)(1.06)⁸  - X

Amount after 8 Years ( 2 Year more) = ((50000 * ( 1.06)⁴ - X)(1.06)⁸  - X )(1.06)⁴

((50000 * ( 1.06)⁴ - X)(1.06)⁸  - X )(1.06)⁴ = X

on Solving we Get X = 29714

Each Daughter will Receive  Rs 29714

Another way to solve

Let 13 year get  = A

15 Year Get = B

19 Year get =  50000 - ( A + B)

Amount of A = Amount of B = Amount of C  

=> A (1.06)¹⁶ = B(1.06)¹²  =  (50000 - ( A + B))(1.06)⁴

B = A (1.06)⁴

A (1.06)¹⁶ =  (50000 - ( A + A(1.06)⁴)(1.06)⁴

=>A(1.06)¹² = 50000 - A (1 + (1.06)⁴)

=> A ( (1.06)¹² +  (1.06)⁴ + 1) = 50000

=> A= 50000 / ( (1.06)¹² +  (1.06)⁴ + 1)

=> A =11,696.8

A (1.06)¹⁶ = 29714  ( at age of 21 Years)

B = 14766.9

C = 23536.3