8-year old Alice gets a weekly allowance from her parents. On her 8th birthday, she was promised by her parents that she would get an additional $1 for the 1st. week, $2 for the 2nd. week, $3 for the 3rd. week.......etc., provided she deposited this money in her College Fund which earns interest of 6% compounded annually. Assume the year to be 52 weeks, how much money would Alice have saved by her 18th birthday, in her College Fund, to go to university? Thanks for any help.
The solution to this question is similar to others in the same vein. There is, however, a rather complicated and rarely used TVM formula just for this type of problem. But, it will much easier task to sum the FV of all 520 payments.
But, before we do that we have to convert the interest rate from yearly compound to weekly compound.
6% comp. annually =5.83015671067 comp. weekly. We divide this nominal rate by 52 to get a weekly rate of =.112118398282%.
Then we simply sum them up on any good calculator, such as Wolfram/Alpha, and it should give the accurate result. This result comes to:
=$165,332.68 - which would be the balance in her College Fund when she turns 18.
I have checked this figure using the above-mentioned formula and they both agree.
Here is the summation using W/A:
http://www.wolframalpha.com/input/?i=sum+n(1.0011211839)%5E(519-n),+n%3D0+to+519
