Question

Steve Hitchcock is 38 years old today and he wishes to accumulate $501,000 by his 61st birthday so he can retire to his summer place on Lake Hopatcong. He wishes to accumulate this amount by making equal deposits on his 38th through his 60th birthdays. What annual deposit must Steve make if the fund will earn 11% interest compounded annually?

Annual Deposit=?

Cindy Ross has $18,800 to invest today at 9% to pay a debt of $40,832. How many years will it take her to accumulate enough to liquidate the debt?

Number of year= ?

Amy Houston has a $29,000 debt that she wishes to repay 6 years from today; she has $17,292 that she intends to invest for the 6 years. What rate of interest will she need to earn annually in order to accumulate enough to pay the debt?

Rate of interest ?

Answer 1

	Future Value of Accumulated Amount = $501000
	Total No. of deposit is [61-38] = 23
	Interest Rate = 11% compounded annually
1	Annuity Future Value = C * [(Future Value Factor - 1)/r]
			= C*[(1+r)^n-1]/r]
	where,
	C = Annuity Cash Amount
	n = no of time periods
	r = rate of return
	Annuity Future Value = C * [(Future Value Factor - 1)/r]
			= C*[(1+r)^n-1]/r]
	$501000 = C *[((1+.11)^23-1)/0.11]
	$501000 = C *[((1.11)^23-1)/0.11]
	$501000 = C *[((1.11)^23-1)/0.11]
	$501000 = C *[(11.02627-1)/0.11]
	$501000 = C *[10.02627/0.11]
	$501000 = C *91.14788
	C = $501000/91.14788
	= $5496.56
	Therefore, the annual deposit amount is $5496.56
2	FV= PV*(1+r)^n
	40,832 = 18,800*(1+9%)^n
	40382/18800 = 1.09^n
	1.09^n = 2.148
	n log 1.09 = log 2.148
	n 0.0374265 = 0.332034
	n = 0.332034/0.0374265
	= 9 years
3	This also a single sum of $ 17292 invested @ ? % to become $ 29000 in 6   years.
	To find the interest % Using compound interest formula,
	FV= Initial amount*(1+r)^n
	29000=17292*(1+r)^6
	29000/17292 = (1+r)^6
	1.6771 = (1+r)^6
	Solving for r   in an online equation solver, we get
	Annual Rate of Interest=   9 %