SOLUTION: Yumi's grandparents presented her with a gift of $18,000 when she was 10 years old to be used for her college education. Over the next 7 years, until she turned 17, Yumi's parents

Question 1124448: Yumi's grandparents presented her with a gift of $18,000 when she was 10 years old to be used for her college education. Over the next 7 years, until she turned 17, Yumi's parents had invested her money in a tax-free account that had yielded interest at the rate of 4.5%/year compounded monthly. Upon turning 17, Yumi now plans to withdraw her funds in equal annual installments over the next 4 years, starting at age 18. If the college fund is expected to earn interest at the rate of 5%/year, compounded annually, what will be the size of each installment? (Assume no interest is accrued from the point she turns 17 until she makes the first withdrawal. Round your answer to the nearest cent.)
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
18000 was invested when yumi was 10 years old.
the investment was for 7 years.
the interest rate was 4.5% per year compounded monthly.

the value of this investment after 7 years was equal to $24,650.14, as shown in the following online calculator display.

$$$

when she turned 18, this amount was invested at 5% per year compounded monthly which she withdrew in monthly installments over the next 4 years.

the payment per month during the 4 year investment period was $567.68 as shown in the following online calculator display.

$$$

the inputs to the first calculator display were:

present value = -18,000 (negative because it's money going out).
future value = 0
number of time periods = 7 * 12 = 84 months.
payment each time period = 0
payment at end of each time period (not used for future value analysis).

click on FV and the calculator tells you that the future value is $24,650.14.

the inputs to the second calculator display were:

present value = $24,650.14 (from the future value of the first calculator display).
future value = 0
number of time periods = 4 * 12 = 48 months.
payment each time period = 0
payment at end of each time period (used this time).

click on PMT and the calculator tells you that the monthly payment is $567.68.

the first use of the calculator found the value of the investment at the end of the 7 year investment period.

the second use of the calculator found the value of each monthly payment for the next 4 years.

i also used excel to provide a month by month analysis.

the critical time periods from the excel analysis are shown below:

$$$

the analysis shows that her monthly installments were $567.68.

that should be your solution.

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