Question

Anna deposited $17,000 in an account that pays 5%, compounded quarterly. She plans to make four consecutive semi-annual withdrawals, the first of which is to occur three years after the deposit. The amount of her uniform, semi-annual withdrawal is closest to...

(please show all work and do not put in an excel. Thank you)

Answer 1

amount deposited = 17000

i = 5% compounded quarterly = 5% / 4 = 1.25% per quarter

effective rate per semiannual period = (1+0.0125)^2 -1 = 2.515625%

Amount deposited for 3 yrs = 3*4 = 12 quarters

Future Amount after 12 quarters = 17000*(F/P,1.25%,12) = 17000 * 1.160754 = 19732.82

Let uniform amount of withdrawl be A for every six months

Present value of withdrawl = A + A*(P/A,2.515625%,3) = A + A*2.855160 = A * 3.855160

Present value of withdrawl = Future Amount

A * 3.855160 = 19732.82

A = 5118.55