Question

Find the amount to which $500 will grow under each of these conditions:

1. 12% compounded annually for 9 years. Do not round intermediate calculations. Round your answer to the nearest cent.

   $  

2. 12% compounded semiannually for 9 years. Do not round intermediate calculations. Round your answer to the nearest cent.

   $  

3. 12% compounded quarterly for 9 years. Do not round intermediate calculations. Round your answer to the nearest cent.

   $  

4. 12% compounded monthly for 9 years. Do not round intermediate calculations. Round your answer to the nearest cent.

   $  

5. 12% compounded daily for 9 years. Assume 365-days in a year. Do not round intermediate calculations. Round your answer to the nearest cent.

   $  

6. Why does the observed pattern of FVs occur?

Answer 1

	Future value		=	Amount*(1+ rate)^time
a)		Amount	=	$500
		time	=	9 years
		rate	=	12% or 0.12
	Future value		=	$500(1+0.12)^9
			=	$500*2.77308
			=	$1,386.54
b)		Amount	=	$500
		time	=	9 years*2 half years per year=18
		rate	=	12%*6/12=6% or 0.06
	Future value		=	$500(1+0.06)^18
			=	$500*2.85434
			=	$1,427.17
c)		Amount	=	$500
		time	=	9 years*4 quaters per year=36
		rate	=	12%*3/12=3% or 0.03
	Future value		=	$500(1+0.03)^36
			=	$500*2.89828
			=	$1,449.14
d)		Amount	=	$500
		time	=	9 years*12 monthsper year=108
		rate	=	12%*1/12=1% or 0.01
	Future value		=	$500(1+0.01)^108
			=	$500*2.92893
			=	$1,464.47
e)		Amount	=	$500
		time	=	9 years*365 days a year=3285
		rate	=	12%*1/365=0.0328767% or 0.000328767
	Future value		=	$500(1+0.000328767)^3285
			=	$500*2.944156
			=	$1,472.08
f)	The obseved pattern of Future values occur because the shorter compounding interval results in higher effective annual return
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