Question

Henna, was lucky. Her parents gave her a car for graduation. Okay, it was a little Hyundai, and definitely not her dream car, but it was serviceable, and Henna didn’t have to worry about buying a new car. In fact, she has been trying to decide how much of her new salary she could save. Neile knows that with a hefty car payment, saving for retirement would be very low on his priority list. Henna believes she could easily set aside $3000 of her $45,000 salary. She is considering putting her savings in a stock fund. She just turned 22 and has a long way to go until retirement at age 65, and she considers this risk level reasonable. The fund she is looking at has earned an average of 9% over the past 15 years and could be expected to continue earning this amount, on average. While she has no current retirement savings, five years ago Henna’s grandparents gave her a new 30-year U.S. Treasury bond with a $10,000 face value.

Henna wants to know her retirement income if she both (1) sells her Treasury bond at its current market value and invests the proceeds in the stock fund and (2) saves an additional $3000 at the end of each year in the stock fund from now until she turns 65. Once she retires, Henna wants those savings to last for 25 years until she is 90.

Queation: Suppose Henna’s Treasury bond has a coupon interest rate of 6.5%, paid semiannually, while current Treasury bonds with the same maturity date have a yield to maturity of 5.4435% (expressed as an APR with semiannual compounding). If she has just received the bond’s 10th coupon, for how much can Henna sell her treasury bond?

Answer 1

Henna Salary	45000	$
Savings	3000	$
Current Age	22	Years
Retirement Age	65	Years
Fund Past Returns	9%
Treasury 30 year bonds
Face Value (FV) =	10000	$
Cupon Rate (R) =	6.50%
YTM	5.44%
10th counpon received =>	5 years completed as the semi annual coupons
Coupon (C)=	325
Remaining Time (T) =	50	(25 Years Semi Annual Coupon)
Bond Value =	5214.531
Retirement Income
1	Value of Bonds		5214.530782
	Invested in Stocks		9% Return for (65-22) years
	Final Value =		212106.8269	$
2	Annual Saving		3000	$
				Years invested	Retirement Age	Current Age
	Total Sum		122028.3295	43	65	22
			111952.5959	42	65	23
			94228.26016	40	65	25
			86447.9451	39	65	26
			79310.04138	38	65	27
			72761.50585	37	65	28
			66753.67509	36	65	29
			61241.90376	35	65	30
			56185.2328	34	65	31
			51546.08514	33	65	32
			47289.98637	32	65	33
			43385.30859	31	65	34
			39803.03541	30	65	35
			36516.54625	29	65	36
			33501.41857	28	65	37
			30735.2464	27	65	38
			28197.47376	26	65	39
			25869.24198	25	65	40
			23733.24952	24	65	41
			21773.62342	23	65	42
			19975.8013	22	65	43
			18326.42321	21	65	44
			16813.2323	20	65	45
			15424.98376	19	65	46
			14151.36125	18	65	47
			12982.90023	17	65	48
			11910.91764	16	65	49
			10927.44738	15	65	50
			10025.18108	14	65	51
			9197.413836	13	65	52
			8437.994345	12	65	53
			7741.279216	11	65	54
			7102.091024	10	65	55
			6515.679838	9	65	56
			5977.687925	8	65	57
			5484.117362	7	65	58
			5031.300333	6	65	59
			4615.871865	5	65	60
			4234.74483	4	65	61
			3885.087	3	65	62
			3564.3	2	65	63
			3270	1	65	64
			3000	0	65	65
	Additional Saving		1341856.521