Yumis grandparents presented her with a gift of 18000 when s

Yumi\'s grandparents presented her with a gift of $18,000 when she was 12 years old to be used for her college education. Over the next 5 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.)

Solution

Using the compound Interest Formula

A = P(1+r)^t

=> 18000(1+0.025)^5

=> 18000 * (1.025)^5

=> $20,365.347

Now plug this value in the annunity formula we get

M = $20,365.347(1 - (1.03)^(-4))

=> 2270.99$