Question

An engineer will deposit 15% of her salary each year into a retirement fund. If her current annual salary is $80,000 and she expects that it will increase by 5% each year, what will be the present worth of the fund after 35 years if it earns 5% per year?

a. $1.3 million

b. $3.4 million

c. $2.2 million

d. $4.5 million

Answer 1

ANSWER:

i have solved in excel as the calculations were very long , there seems to be a mistake in the options given as the options given are for future worth and not the present worth and so i have solved for both present worth and future worth in excel. please ask your teacher again regarding the options as the present worth is $400,000 while the future worth is $2,206,406.15 which is option c given in the question.

year	0	1	2	3	4	5	6	7	8	9	10	11	12	13	14	15	16	17	18	19	20	21	22	23	24	25	26	27	28	29	30	31	32	33	34	35
salary		80,000.00	84,000.00	88,200.00	92,610.00	97,240.50	102,102.53	107,207.65	112,568.03	118,196.44	124,106.26	130,311.57	136,827.15	143,668.51	150,851.93	158,394.53	166,314.25	174,629.97	183,361.47	192,529.54	202,156.02	212,263.82	222,877.01	234,020.86	245,721.90	258,008.00	270,908.40	284,453.82	298,676.51	313,610.33	329,290.85	345,755.39	363,043.16	381,195.32	400,255.08	420,267.84
deposit in retirement fund		12,000.00	12,600.00	13,230.00	13,891.50	14,586.08	15,315.38	16,081.15	16,885.21	17,729.47	18,615.94	19,546.74	20,524.07	21,550.28	22,627.79	23,759.18	24,947.14	26,194.50	27,504.22	28,879.43	30,323.40	31,839.57	33,431.55	35,103.13	36,858.29	38,701.20	40,636.26	42,668.07	44,801.48	47,041.55	49,393.63	51,863.31	54,456.47	57,179.30	60,038.26	63,040.18
present worth	400,000.00
future worth	2,206,406.15

salary increases by 5% per year.

deposit is 15% of the salary every year.

present worth is found out by using the npv function in excel.

=npv(rate,cash flow from year 1 to year 35)

=npv(5%, cash flow from year 1 to year 35)

future worth is found out by using the fv function in excel.

=-fv(rate,nper,pmt,pv)

=-fv(5%,35,,400000) = 2,206,406.15