Question 1139199: Parents want to help their daughters save for the future by giving them 1/4
of the money in their savings accounts every four months until age 18.
Mindy and Julie are 14 and 10, respectively; each has $10 in her account.
The girls prefer to receive $100 the first year, $110 the second, $120 the
third, etc. Ignoring interest, which option is best for each girl? Please help me. I have no idea how to solve this problem!
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! what the girls want to get and what the parents want to give is modeled in the following excel spreadsheet.
what the girls want is 100 at the end of the first year, 110 at the end of the second year, 120 at the end of the third year, etc.....
column D shows what the girls will get at the end of each year.
column E shows the additional amount that the girls get each year over the previous year.
at the end of the first year, they get an additional 100.
at the end of the second year, they get an additional 110.
etc.....
column G shows what the parents want to give.
the parents want to give them 1/4 of the amount in their account at the end of each quarter.
1/4 is 25% = .25
that means the money grows to 1.25 the amount of the previous quarter, every quarter.
at the end of the first quarter, the amount becomes 10 * 1.25.
at the end of the second quarter, the amount becomes 10 * 1.25 * 1.25 = 10 * 1.25^2.
at the end of the third quarter, the amount becomes 10 * 1.25 * 1.25 * 1.25 = 10 * 1.25^3.
at the end of the fourth quarter, the amount becomes 10 * 1.25 * 1.25 * 1.25 * 1.25 = 10 * 1.25^4.
every additional year, the amount is multiplied by another 1.25^4.
this is shown in the spreadsheet.
at the end of year 0, the amount is 10.
at the end of year 1, the amount is 10 * 1.25^4 = $24.41.
at the end of year 2, the amount is 10 * 1.25^4 * 1.25^4 = 10 * 1.25^8 = $59.60.
at the end of year 3, the amount is 10 * 1.25^4 * 1.25^4 * 1.25^4 = 10 * 1.25^12 = $145.52.
at the end of year 4, the amount is 10 * 1.25^4 * 1.25^4 * 1.25^4 * 1.25^4 = 10 * 1.25^16 = $355.27.
at the end of the 4th year:
what the girls want is equal to $470.
what the parents want to give is equal to $355.27.
at the end of the 8th year:
what the girls want is equal to $1,090.
what the parents want to give is equal to $12,621.77.
mindy gets hers at the end of the 4th year because she was 14 years old when this started, so she would be better off with what the girls want.
jill gets hers at the end of the 8th year because she was 10 yers old when this started, so she would be much better off with what the parents want to give.
the biggest difference between the two methods is in the compounding of the balance with what the parents want to give as opposed to just adding a litle additional each year with what the girls want.
each year, the balance is multiplied by 1.25^4 with what the parents want to give.
this really starts to take off after the 4th year.
the balance at the end of the 4th year is $355.27.
the year after that the balance becomes $355.27 * 1.25^4 = $867.36.
note that 1.25^4 is equal to 2.44140625, so the balance is mmultiplied by that factor at the end of every year.
$355.27 * 2.44... = $867.36
$867.36 * 2.44... = $2117.58
etc.....
the bigger the balance, the bigger the growth, as can be seen in column H.
any questions, write to dtheophilis@gmail.com
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