Question

A father lefta will of $45 between his two daugthers aged 8,5years and 16 years such that they will get equal amounts when each of them reach the age 20 years. The original amount of $45 was invesed at 10% per annum simple interest. How much did the elder daughter get at the time of the will?

Answer 1

The father gives the older and younger daughters A and B amounts respectively.
From the question, it is known that A + B = 45.
The money after x years can be calculated by the formula:
Q = (P)*1.1^x
Where Q is money after interest and P is money before interest.
The older daughter will have to wait 4 years and therefore will have
$(A*1.1^4) when she turns 20
The younger daughter will have to wait 11.5 years and will have
$(B*1.1^11) when she turns 20
Note that it isn't 1.1^(11.5) because interest is only applied at the end of the year.

Because both daughters receive the same amount at the ages of 20:
A*1.1^4 = B*1.1^11
A*1.1^4 = (45-A)*1.1^11
A*(1.1^4+1.1^11) = 45*1.1^11
A = 45*1.1^11/(1.1^4+1.1^11) = 29.73
B = 45-A = 15.27

So the older and younger daughters are originally given $29.73 and $15.27 respectively.