On January 1, 2005, a person’s savings account was worth $250,000. Every month thereafter, this person...

On January 1, 2005, a person’s savings account was worth $250,000. Every month thereafter, this person makes a cash contribution of $750 to the account. If the fund is expected to be worth $500,000 on January 1, 2010, what annual rate of interest is being earned on this fund?

Expert Solution

The answer is 11.12%

Calculations and explanations:

Here monthly payment = $750, total duration = 5 years*12 = 60 months, PV = 250,000 and FV = 500,000

The 1st contribution is made 1 month after January 1, 2005 i.e. at end of the month, Hence we can see that for January interest will be earned only on 250,000 and the contribution of 750 will not earn any interest. Closing amount at the end of January 2005 = 250,000+750+interest on 250,000

For February 2005 interest = interest rate*closing balance on January 2005. We will continue this cycle till end of December 2009.

Creating a table we get month rate = 0.927% and so annual rate = 0.927%*12 = 11.12%

Date	Beginning balance	Contribution	r (monthly)	Interest amount	Ending balance
01 January 2005	250,000.00	750.00	0.927%	2,316.94	253,066.94
01 February 2005	253,066.94	750.00		2,345.36	256,162.30
01 March 2005	256,162.30	750.00		2,374.05	259,286.34
01 April 2005	259,286.34	750.00		2,403.00	262,439.34
01 May 2005	262,439.34	750.00		2,432.22	265,621.56
01 June 2005	265,621.56	750.00		2,461.71	268,833.28
01 July 2005	268,833.28	750.00		2,491.48	272,074.75
01 August 2005	272,074.75	750.00		2,521.52	275,346.27
01 September 2005	275,346.27	750.00		2,551.84	278,648.11
01 October 2005	278,648.11	750.00		2,582.44	281,980.55
01 November 2005	281,980.55	750.00		2,613.32	285,343.87
01 December 2005	285,343.87	750.00		2,644.49	288,738.37
01 January 2006	288,738.37	750.00		2,675.95	292,164.32
01 February 2006	292,164.32	750.00		2,707.70	295,622.03
01 March 2006	295,622.03	750.00		2,739.75	299,111.78
01 April 2006	299,111.78	750.00		2,772.09	302,633.87
01 May 2006	302,633.87	750.00		2,804.73	306,188.60
01 June 2006	306,188.60	750.00		2,837.68	309,776.28
01 July 2006	309,776.28	750.00		2,870.93	313,397.21
01 August 2006	313,397.21	750.00		2,904.49	317,051.69
01 September 2006	317,051.69	750.00		2,938.35	320,740.05
01 October 2006	320,740.05	750.00		2,972.54	324,462.58
01 November 2006	324,462.58	750.00		3,007.04	328,219.62
01 December 2006	328,219.62	750.00		3,041.86	332,011.47
01 January 2007	332,011.47	750.00		3,077.00	335,838.47
01 February 2007	335,838.47	750.00		3,112.47	339,700.94
01 March 2007	339,700.94	750.00		3,148.26	343,599.20
01 April 2007	343,599.20	750.00		3,184.39	347,533.59
01 May 2007	347,533.59	750.00		3,220.85	351,504.44
01 June 2007	351,504.44	750.00		3,257.65	355,512.09
01 July 2007	355,512.09	750.00		3,294.80	359,556.89
01 August 2007	359,556.89	750.00		3,332.28	363,639.17
01 September 2007	363,639.17	750.00		3,370.11	367,759.28
01 October 2007	367,759.28	750.00		3,408.30	371,917.58
01 November 2007	371,917.58	750.00		3,446.84	376,114.42
01 December 2007	376,114.42	750.00		3,485.73	380,350.15
01 January 2008	380,350.15	750.00		3,524.99	384,625.14
01 February 2008	384,625.14	750.00		3,564.61	388,939.75
01 March 2008	388,939.75	750.00		3,604.59	393,294.34
01 April 2008	393,294.34	750.00		3,644.95	397,689.29
01 May 2008	397,689.29	750.00		3,685.68	402,124.98
01 June 2008	402,124.98	750.00		3,726.79	406,601.77
01 July 2008	406,601.77	750.00		3,768.28	411,120.05
01 August 2008	411,120.05	750.00		3,810.16	415,680.21
01 September 2008	415,680.21	750.00		3,852.42	420,282.62
01 October 2008	420,282.62	750.00		3,895.07	424,927.70
01 November 2008	424,927.70	750.00		3,938.12	429,615.82
01 December 2008	429,615.82	750.00		3,981.57	434,347.39
01 January 2009	434,347.39	750.00		4,025.42	439,122.81
01 February 2009	439,122.81	750.00		4,069.68	443,942.48
01 March 2009	443,942.48	750.00		4,114.35	448,806.83
01 April 2009	448,806.83	750.00		4,159.43	453,716.26
01 May 2009	453,716.26	750.00		4,204.93	458,671.18
01 June 2009	458,671.18	750.00		4,250.85	463,672.03
01 July 2009	463,672.03	750.00		4,297.19	468,719.22
01 August 2009	468,719.22	750.00		4,343.97	473,813.19
01 September 2009	473,813.19	750.00		4,391.18	478,954.37
01 October 2009	478,954.37	750.00		4,438.83	484,143.20
01 November 2009	484,143.20	750.00		4,486.92	489,380.12
01 December 2009	489,380.12	750.00		4,535.45	494,665.57
01 January 2010	494,665.57	750.00		4,584.43	500,000.00

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