Dividing Money Among Children

A family has 5,000 € to divide between their two children aged 10 and 14. They will open an account for each child at the same bank, compounded quarterly at a fixed annual interest rate of 2.75%. Determine how the family must split the available sum between the two accounts if they want both children to have the same amount of money when each reaches the age of 18.

Final Answer:

a =  2364.4896
b =  2635.5104

Step-by-step explanation:


5000 = a+b
a · 1.0275^(18-10) = b · 1.0275^(18-14)

a+b = 5000
1.242381a-1.114621b = 0

Pivot: Row 1 ↔ Row 2
1.24a-1.11b = 0
a+b = 5000

Row 2 - 1/1.24238055 · Row 1 → Row 2
1.24a-1.11b = 0
1.9b = 5000


b = 5000/1.89716573 = 2635.51038857
a = 0+1.1146212594141b/1.24238055 = 0+1.11462126 · 2635.51038857/1.24238055 = 2364.48961143

a = 2364.489611
b = 2635.510389

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You need to know the following knowledge to solve this word math problem:

algebraarithmeticbasic operations and conceptsUnits of physical quantitiesGrade of the word problem

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