FUTURE VALUE FOR VARIOUS COMPOUNDING PERIODS Find the amount to which $800 will

ID: 2812855 • Letter: F

Question

FUTURE VALUE FOR VARIOUS COMPOUNDING PERIODS

Find the amount to which $800 will grow under each of these conditions:

8% compounded annually for 8 years. Do not round intermediate calculations. Round your answer to the nearest cent.
$

8% compounded semiannually for 8 years. Do not round intermediate calculations. Round your answer to the nearest cent.
$

8% compounded quarterly for 8 years. Do not round intermediate calculations. Round your answer to the nearest cent.
$

8% compounded monthly for 8 years. Do not round intermediate calculations. Round your answer to the nearest cent.
$

8% compounded daily for 8 years. Do not round intermediate calculations. Round your answer to the nearest cent.
$

Why does the observed pattern of FVs occur?

Future value at 8% compounded annually = principal * (1 + interest rate)^(number of years)

= $ 800 * 1.08^8 = $1480.74

Future value at 8% compunded semiannually = principal * (1 + interest rate/2)^(2* number of years)

= 800 * (1.04)^16 = $1498.38

Future value at 8% compounded quaterly = principal * (1 + interest rate/4)^(4* number of years)

= 800 * (1.02)^32 = $1507.63

Future value at 8% compounded monthly = principal * (1 + interest rate/12)^(12* number of years)

= 800 * (1 + .08/12)^(12*8) = $1513.97

Future value at 8% compounded daily = principal * (1 + interest rate/365)^(365* number of years)

= $1517.08

Due to increase in number of compounding, future value increases since it takes compounding period at lesser interval of time.

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