You and your statistics-major friend are curious how much rate of returns and compounding impacts an investment over

Question

You and your statistics-major friend are curious how much rate of returns and compounding impacts an investment over the course of someone’s career. What is the difference in retirement savings if you invest $100 at the end of each month and earn a 8% return (compounded monthly), and if you invested $1,200 at the end of each year and earned 7% (compounded annually)? Both are for a duration of 50 years. $274,458 $298,476 $301,478 $305,338 $253,436

Help In Homework · Accepted Answer

Step1 : Future value of monthly compounding annuity Future Value of an Ordinary Annuity = C*[(1+i)^n-1]/i Where, C= Cash Flow per period i = interest rate per period =8%/12 =0.666667% n=number of period =50*12 =600 = $100[ (1+0.006666667)^600 -1] /0.006666667 = $100[ (1.006666667)^600 -1] /0.006666667 = $100[ (53.8782 -1] /0.006666667] = $793,172.87 Step 2 : Future value of annual compounding annuity Future Value of an Ordinary Annuity = C*[(1+i)^n-1]/i Where, C= Cash Flow per period i = interest rate per period n=number of period = $1200[ (1+0.07)^50 -1] /0.07 = $1200[ (1.07)^50 -1] /0.07 = $1200[ (29.457 -1] /0.07] = $487,834.72 Step 3 : Difference =$793172.87-487834.72 = $305338

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You and your statistics-major friend are curious how much rate of returns and compounding impacts an investment over the course of someone’s career

Expert Solution

Archived Solution

Step1 :	Future value of monthly compounding annuity
	Future Value of an Ordinary Annuity
	= C*[(1+i)^n-1]/i

	Where,
	C= Cash Flow per period
	i = interest rate per period =8%/12 =0.666667%
	n=number of period =50*12 =600

	= $100[ (1+0.006666667)^600 -1] /0.006666667

	= $100[ (1.006666667)^600 -1] /0.006666667

	= $100[ (53.8782 -1] /0.006666667]

	= $793,172.87

Step 2 :	Future value of annual compounding annuity

	Future Value of an Ordinary Annuity
	= C*[(1+i)^n-1]/i

	Where,
	C= Cash Flow per period
	i = interest rate per period
	n=number of period

	= $1200[ (1+0.07)^50 -1] /0.07

	= $1200[ (1.07)^50 -1] /0.07

	= $1200[ (29.457 -1] /0.07]

	= $487,834.72

Step 3 :	Difference =$793172.87-487834.72
	= $305338