Amortization Math Help

Yumi's grandparents presented her with a gift of $12,000 when she was 8 yr old to be used for her college education. Over the next 9 yr, 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 yr, starting at age 18. If the college fund is expected to earn interest at the rate of 6%/year, compounded annually, what will be the size of each installment? (Round your answer to the nearest cent.)

Can you also provide the formula that was used. Thanks!

12000 invested for 9 years grows to 12000(1 + .045/12)^(9x12) = A
The formula for an annuity of 1 withdrawn at the end of each year from a 6% account is as follows:
Let v= 1/1.06. That's the present value of $1 discounted 1 year.
The annuity factor is v + v^2 + v^3 + v^4 = v(1 + v + v^2 + v^3) = v(1 - v^4) / (1 - v)
Now v/(1 - v) = 1(1/v - 1) = 1/(1+i - 1) = i
So the annuity factor is just (1 + v^4)/i

This should work out to
12000
x
1.498167236
=
17978.00683
div by
3.465105613
=
5188.29982

You should check the math.

Age 8: $12,000
Age 17: $12,000(1 + 0.045/12)^(12*(17-8)) = $12,000(1.00375)^108. Call this amount "A".

Beginning at age 18, she will withdraw 4 equal installments. Each installment, P =

P = 0.06 * A / (1 - (1.06)^-4)

Plug & play