Question 1200915: Yumi's grandparents presented her with a gift of $19,000 when she was 9 years old to be used for her college education. Over the next 8 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 2.5%/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 3%/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! she got 19000 when she was 9.
that was invested at 2.5% per year, compounded monthly, until she turned 17.
thhat's the future value of 19000 * (1 + .025/12) ^ (8 * 20 = 23201.82.
she will have 23,201.82 available to her when she turns 17.
she puts that money in a college fund that is earning 3% per year, compounded annually.
she will be withdrawing from that fun for the next 4 years.
the amount that she can withdraw at the end of each year is equal to 6241.92
here are what the clculations look like, usimng the financial calculator at https://arachnoid.com/finance/
first the investment of 19000 at 2.5% interest per year, compounded monthly, for 8 years.
the initial investment is negative because it is money going out.
the future value of the investment is positive because it is money coming in.
the annual interest rate of 2.5% per year is divided by 12 to get the monthly interest rate.
the number of years is multiply by 12 to get the number of months.
next the withdrawal at 3% interest per year, compounded annually, for 4 years.
the future vlaue of the investment is placed into the present value field.
it is positive, because it is money coming.
the payment at the end of each year is negative because it is money going out.
the number of years is 4 and the interest rate per year is 3%.
note that she starts earning interest as soon as she puts her money into the college fund.
if the money is invested when she turns 17, she will have earned 3% interest by the end of that year.
this is what the yearly transactions look like in excel.
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