Question 1203655: Yumi's grandparents presented her with a gift of $19,000 when she was 8 years old to be used for her college education. Over the next 9 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! you can use the calculator at https://arachnoid.com/finance/ to solve this.
there are formulas you can use as well.
if you need formulas, i can supply them.
the procedure is the same.
you put your inputs into the calculator or the formula, and you get your answer by applying the formula or using the calculator to solve the problem.
this method uses the calculator.
there are two sections.
the first section is to get the future value of the 19000 at the point where that becomes the input to the second section.
here are the results of the calculations.
the present value is set to -19,000.
the future value is set to 0.
the number of time periods is set to 9 * 12 = 108
the payment amount is set to 0.
the interest rate per time period is set to 4.5% per year /12 months per year = .375% per month.
the payment at the end or the beginning of each time period is not used because there is no payment in each time period.
the future value is calculated to be 28,465.18.
the present value is set to -28,465.18
the future value is set to 0
the number of time periods is set to 4
the interest rate per time period is set to 5%
payment is made at the beginning of each time period.
the payment at the beginning of each month is calculated to be 7,645.25.
the next two pictures are of the excel spreadsheet that i used to confirm the calculations were correct by calculating the month by month and year by year remaining balances.
note:
the assumption that she earns no interest from the time she turns 17 until the time she makes the first withdrawal is not reasonable.
unless there is a reason why she could not do it, she could investment the money into the college fund when she turns 17 and then withdraw the money at the end of each year rather than at the beginning of each year.
if she did that, she would be able to withdraw 8,027.52 at the end of each year, rather than 7,645.25 at the beginning of each year.
the differrence is she invested in the fund when she turned 17 rather than when she turned 18.
doing it that way, she would have earned 5% on her money between when she turned 17 and when she turned 18.
the calculator inputs would be the same except you would tell it to make the yearly payments at the end of each year rather than at the beginning of each year.
here's what that would look like.
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