Question

Starting six months after her grandson​ Robin's birth, Mrs. Devine made deposits of ​$210 into a trust fund every six months until Robin was twenty-one years old. The trust fund provides for equal withdrawals at the end of each six months for three ​years, beginning six months after the last deposit. If interest is 6.9​% compounded semi-annually​, how much will Robin receive every six months​?

Robin will receive ​$_?. ​(Round the final answer to the nearest cent as needed. Round all intermediate values to six decimal places as​ needed.)

Answer 1

	Step 1:	Future value of $210 annuity at the end of 21th years
		Future Value of an Ordinary Annuity
		= C*[(1+i)^n-1]/i
		Where,
		C= Cash Flow per period
		i = interest rate per period =6.9%/ 2=3.45%
		n=number of period =21*2 =42
		= $210[ (1+0.0345)^42 -1] /0.0345
		= $210[ (1.0345)^42 -1] /0.0345
		= $210[ (4.1561 -1] /0.0345]
		= $19,210.74
	Step 2:	Sim monthly withdrwal
		Present Value Of An Annuity
		= C*[1-(1+i)^-n]/i]
		Where,
		C= Cash Flow per period
		i = interest rate per period
		n=number of period
		$19210.74= C[ 1-(1+0.0345)^-6 /0.0345]
		19210.74= C[ 1-(1.0345)^-6 /0.0345]
		19210.74= C[ (0.1841) ] /0.0345
		C= $812.36
		Six monthly withdrawal= $812.36