natalie's family has decided that in 3 months they will start depositing $160 every 3 months for 3 yrs. the account will earn interest at 5.7% per annum, compounded quarterly. then 3 months after the last deposit, they plan to withdraw money every 3 months for 24 equal payments for music lessons for natalie. how much will each withdrawal be?

Question

anonymous · Answer

this is how i approached to answer the question:
first, i decided that i should look for the amount after the last deposit.
R=160
n= 4x3=12
i= 0.057/4= 0.01425

PV = R [1-(1+i)^-n/ i]
PV = 160 [1-(1-.01425)^-12/0.01425]
PV = 160 [1-(0.843839408)/0.01425]
PV = 160 [0.156160591/0.01425]
PV = 160 [10.95863803]
PV = 1753.38

Then i decided to find the withdrawals.
PV=1753.38
R=?
n=24
i=0.01425

1753.38 = R [1-(1.01425)^-24/0.01425]
			= R [ 1-0.712064946/0.01425]
			= R [ 0.287935053/0.01425]
		R	= 1753.38(0.01425)/0.287935053
			= 24.985665/0.287935053
			= 86.78

anonymous · Answer

however the answer should be $102.83

what am i doing wrong?