Education IRA: On January 1, 1999, John’s parents decided to place $45 at the end of each month into an Education IRA.
(a) Find a recursive formula that represents the balance at the end of each month if the rate of return is assumed to be 6% per annum compounded monthly.
(b) How long will it be before the value of the account exceeds $4000?
(c) What will be the value of the account in 16 years when John goes to college?
(a) The recursive formula for interest compounded annually is:
(b) The value of account exceeds $4,000 after 75 months.
(c) The value of account in 192 months will be $14,216.36.
After the end of every month, John's parents' deposit $45 i.e., A=$45.
The interest rate compounded quarterly, r = 6.
Using the compound interest formula as:
Using a graphing calculator to compute the account value exceeding $4,000 gives:
Number of months in 16 years:
The amount in the account after 192 months will be:
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