If I have four children and I want to ensure each have £8,500 come there 18th birthday, assuming that I put money in each month, and gain 10% interest per year (taking into account compound interest). What is the most cost effective way I need to pay each month?
Compounded each year
Name | Age | Initial Deposit (£)
Child A | 10 years 5 months | 1,000
Child B | 8 Years 10 months | 960
Child C | 5 Years 2 months | 440
Child D | 1 Year 6 months | 190
What I mean is, when child A becomes 18, the monthly funds usually used for them could then be divided among the other 3 children?
So I know Child D needs £15.01 a month for 16 years and 6 months, but can this be underpaid and then overpaid when other children are no longer receiving monthly money?
What is the best and most efficient calculation? sorry I don't even know what type of maths question this is
If each account has 8500 in it on their 18th birthday, the present value of these accounts will be $8500(\frac {1}{1.1^{7.58}} + \frac {1}{1.1^{9.17}} + \frac {1}{1.1^{16.5}})$
We will then need the present value of the current contributions to equal the present value of the benefit. If we make equal contributions over the next 16.5 years.
$P = FV \frac {1.1^{16.6}}{1.1^{16.5} - 1}$
After that, it doesn't matter which account you contribute to each time you make a contribution so long as you don't overfund one account at the expense of the others.