Question

pts) 4. Evangeline is 24 years old today. She recently graduated with a finance degree and obtained a job as a financial adviser to a large company. She currently has an annual salary of $150,000. She expects her salary to increase at an average rate of 6% per year as long as she works. She plans to save for her retirement and has decided to make annual contributions to a retirement-savings account. She will make her first contribution when she turns 25 and she intends to deposit 12% of this year's salary at that time. Likewise, she expects to deposit 12% of her salary every year thereafter until the age of 65, when she plans to retire. Assume that the interest rate is 8%. (15pts) (a)What is the present value (at age 24) of her retirement savings? Draw a timeline. (5pts) (b)How much will she have in her retirement-savings account on her 65th birthday?

Answer 1

Annual salary increase = 6%, Contribution each year = 12%, Interest rate = 8%.

Contribution or investment at age 25 = $ 18000

Contribution or investment at age 26 = $ 18000 * 1.12

similarly every year contribution can be calculated by = $ 18000 * (1+ contribution rate)^n

= $ 18000 * 1.12^n

NPV= Cash flow/(1+i)^t −initial investment, where:i=Required return or discount rate, t=Number of time periods​

Table:-

			Annual Salary	$150,000	$159,000	$168,540	$178,652.40	$189,371.54	$200,733.84	$212,777.87	$225,544.54	$239,077.21	$253,421.84	$268,627.15	$284,744.78	$301,829.47	$319,939.24	$339,135.59	$359,483.73	$381,052.75	$403,915.92	$428,150.87	$453,839.93	$481,070.32	$509,934.54	$540,530.61	$572,962.45	$607,340.20	$643,780.61	$682,407.44	$723,351.89	$766,753.00	$812,758.18	$861,523.68	$913,215.10	$968,008.00	$1,026,088.48	$1,087,653.79	$1,152,913.02	$1,222,087.80	$1,295,413.07	$1,373,137.85	$1,455,526.12	$1,542,857.69	$1,635,429.15
			Age	24	25	26	27	28	29	30	31	32	33	34	35	36	37	38	39	40	41	42	43	44	45	46	47	48	49	50	51	52	53	54	55	56	57	58	59	60	61	62	63	64	65
Annual Salary increase	6%		Contribution		$18,000	$19,080	$20,225	$21,438	$22,725	$24,088	$25,533	$27,065	$28,689	$30,411	$32,235	$34,169	$36,220	$38,393	$40,696	$43,138	$45,726	$48,470	$51,378	$54,461	$57,728	$61,192	$64,864	$68,755	$72,881	$77,254	$81,889	$86,802	$92,010	$97,531	$103,383	$109,586	$116,161	$123,131	$130,518	$138,350	$146,651	$155,450	$164,777	$174,663	$185,143
Contribution	12%		savings at year end		$18,000	$38,520	$61,826	$88,211	$117,992	$151,520	$189,175	$231,374	$278,573	$331,270	$390,006	$455,376	$528,026	$608,661	$698,050	$797,032	$906,521	$1,027,512	$1,161,091	$1,308,440	$1,470,843	$1,649,703	$1,846,543	$2,063,021	$2,300,944	$2,562,273	$2,849,144	$3,163,878	$3,508,998	$3,887,249	$4,301,612	$4,755,327	$5,251,914	$5,795,197	$6,389,332	$7,038,828	$7,748,585	$8,523,921	$9,370,611	$10,294,923	$11,303,660
Interest rate	8%		NPV at age 24	$481,775.94
			FV of each contributon at age 65		391041.3869	383799.88	376692.4746	369716.688	362870.083	356150.2663	349554.891	343081.6523	336728.2884	330492.5793	324372.3464	318365.4511	312469.7946	306683.3169	301003.9962	295429.8482	289958.925	284589.3153	279319.1428	274146.5661	269069.7778	264087.0042	259196.5041	254396.5688	249685.5213	245061.7153	240523.5354	236069.3958	231697.7404	227407.0415	223195.8	219062.5444	215005.8306	211024.2412	207116.3849	203280.8962	199516.4352	195821.6864	192195.3589	188636.1856	185143
			Retirement savings at age 65		11303660.06
	Timeline of retirement savings			Age	25	26	27	28	29	30	31	32	33	34	35	36	37	38	39	40	41	42	43	44	45	46	47	48	49	50	51	52	53	54	55	56	57	58	59	60	61	62	63	64	65
				savings at year end	$18,000	$38,520	$61,826	$88,211	$117,992	$151,520	$189,175	$231,374	$278,573	$331,270	$390,006	$455,376	$528,026	$608,661	$698,050	$797,032	$906,521	$1,027,512	$1,161,091	$1,308,440	$1,470,843	$1,649,703	$1,846,543	$2,063,021	$2,300,944	$2,562,273	$2,849,144	$3,163,878	$3,508,998	$3,887,249	$4,301,612	$4,755,327	$5,251,914	$5,795,197	$6,389,332	$7,038,828	$7,748,585	$8,523,921	$9,370,611	$10,294,923	$11,303,660

Also FV = C₀*(1+r)^t

a) Present value(at age 24) of her retirement savings is $ 481,775.94

b) Retirement savings account balance on her 65th birthday is $ 11,303,660.06

Please refer the table above for detailed calculations.