Question

After receiving an inheritance of $30,000 on her 21st birthday, Julia deposited the inheritance in a savings account with an effective annual interest rate of 6%. She decided to make regular deposits, beginning with $1,000 on her 22nd birthday, and increasing by $250 each year (that is, $1,250 on her 23rd birthday, $1,500 on her 24th birthday, etc.) What is the future worth of Julia’s deposits on her 58th birthday?

Answer 1

Solution:

Statement of interest and deposit balance at the end o year
Age	Opening Balance	Investment	Interest (Opening Balance*6%)	Closing Balance (Opening + Investment + Interest)
21	$0.00	$30,000.00	$0.00	$30,000.00
22	$30,000.00	$1,000.00	$1,800.00	$32,800.00
23	$32,800.00	$1,250.00	$1,968.00	$36,018.00
24	$36,018.00	$1,500.00	$2,161.08	$39,679.08
25	$39,679.08	$1,750.00	$2,380.74	$43,809.82
26	$43,809.82	$2,000.00	$2,628.59	$48,438.41
27	$48,438.41	$2,250.00	$2,906.30	$53,594.72
28	$53,594.72	$2,500.00	$3,215.68	$59,310.40
29	$59,310.40	$2,750.00	$3,558.62	$65,619.03
30	$65,619.03	$3,000.00	$3,937.14	$72,556.17
31	$72,556.17	$3,250.00	$4,353.37	$80,159.54
32	$80,159.54	$3,500.00	$4,809.57	$88,469.11
33	$88,469.11	$3,750.00	$5,308.15	$97,527.26
34	$97,527.26	$4,000.00	$5,851.64	$107,378.89
35	$107,378.89	$4,250.00	$6,442.73	$118,071.63
36	$118,071.63	$4,500.00	$7,084.30	$129,655.92
37	$129,655.92	$4,750.00	$7,779.36	$142,185.28
38	$142,185.28	$5,000.00	$8,531.12	$155,716.40
39	$155,716.40	$5,250.00	$9,342.98	$170,309.38
40	$170,309.38	$5,500.00	$10,218.56	$186,027.94
41	$186,027.94	$5,750.00	$11,161.68	$202,939.62
42	$202,939.62	$6,000.00	$12,176.38	$221,116.00
43	$221,116.00	$6,250.00	$13,266.96	$240,632.96
44	$240,632.96	$6,500.00	$14,437.98	$261,570.93
45	$261,570.93	$6,750.00	$15,694.26	$284,015.19
46	$284,015.19	$7,000.00	$17,040.91	$308,056.10
47	$308,056.10	$7,250.00	$18,483.37	$333,789.47
48	$333,789.47	$7,500.00	$20,027.37	$361,316.83
49	$361,316.83	$7,750.00	$21,679.01	$390,745.84
50	$390,745.84	$8,000.00	$23,444.75	$422,190.59
51	$422,190.59	$8,250.00	$25,331.44	$455,772.03
52	$455,772.03	$8,500.00	$27,346.32	$491,618.35
53	$491,618.35	$8,750.00	$29,497.10	$529,865.45
54	$529,865.45	$9,000.00	$31,791.93	$570,657.38
55	$570,657.38	$9,250.00	$34,239.44	$614,146.82
56	$614,146.82	$9,500.00	$36,848.81	$660,495.63
57	$660,495.63	$9,750.00	$39,629.74	$709,875.37
58	$709,875.37	$10,000.00	$42,592.52	$762,467.89

Therefore future worth of Julia's deposits on her 58th birthday is $762,467.89.