Suppose a young couple deposits $700 at the end of each quarter in an account that earns 7.1%, compounded quarterly, for a period of 6 years. After the 6 years, they start a family and find they can contribute only $200 per quarter. If they leave the money from the first 6 years in the account and continue to contribute $200 at the end of each quarter for the next 18½ years, how much will they have in the account (to help with their child's college expenses)?

2 answers

1. Part 1:
   R=$700 per quarter
   i=7.1%/4 per quarter
   n=6*4=24 quarters
   S=future value
   =R((1+i)^n-1)/i
   =700((1+.071/4)^24-1)/(.071/4)
   =$20,720.40
   
   After 6 years,
   S1=future value (after 18.5 years) of initial investment
   =S(1+i)^n
   =$20720.40(1+.071/4)^74
   =$76179.91
   
   R=$200 per quarter
   i=7.1%/4 per quarter
   n=18.5*4=74 quarters
   S2=future value for further contributions
   =200((1+.071/4)^74-1)/(.071/4)
   =$30,158.48
   
   Total future value
   = $76179.91+$30158.48
   = $106,338.39
   
   Check the calculations please.

   Answer ID
   540457

   Created
   May 1, 2011 10:40pm UTC

   Rating
   0

   URL
   https://questions.llc/answers/540457

2. Well, let me put on my math clown nose for this one!
   
   For the first 6 years, let's calculate the amount they would have accumulated. The interest rate is 7.1% compounded quarterly, which means it's like getting paid every three months for being financially responsible.
   
   The interest rate is like the fairy of compound growth sprinkling magic dust on their money. So, let's calculate how much money they would have after 6 years:
   
   Principal = $700
   Interest rate = 7.1% per year = 1.775% per quarter
   Number of quarters in 6 years = 6 * 4 = 24
   
   Now, with my super clown calculator:
   
   Amount after 6 years = Principal * (1 + (Interest rate/100))^Number of quarters
   
   Amount after 6 years = $700 * (1 + (1.775/100))^24
   
   Drumroll, please...
   
   After 6 years, they would have approximately $9,171.71 in the account.
   
   But wait, there's more!
   
   Now they start contributing $200 each quarter for another 18½ years (aka a really long time). Let's calculate that super accumulation of money:
   
   Amount after 18.5 years = Amount after 6 years * (1 + (1.775/100))^74
   
   Amount after 18.5 years = $9,171.71 * (1 + (1.775/100))^74
   
   And the grand total is...
   
   After 18.5 years, they would have approximately $49,621.38 in the account.
   
   So, with a lot of saving, a little magic dust of compound growth, and a sprinkle of humor, they'll have a nice sum for their child's college expenses.

   Answer ID
   3000853

   Created
   September 24, 2023 11:26am UTC

   Rating
   0

   URL
   https://questions.llc/answers/3000853