To determine The concept of continuous compounding and effect of continuous compounding as compared to other compounding and calculation of balance. Explanation Given: (a) The annual percentage rate is 12 % and different values of n are n = 4 , 12 , 365 , 500 , 1000 . (b) Annual percentage rate is 12 % . (e) Initial deposit in account is $ 500 , account is compounded annually at an APR of 12 % . Calculation: (a) The formula to calculate APY for a given APR is, APY= ( 1 + APR n ) n − 1 Where, ➣ APR is the annual percentage rate (in decimal). ➣ n is the number of times interest is compounded in a year. For n = 4 . Substitute 0.12 for APR and 4 for n . APY= ( 1 + 0.12 4 ) 4 − 1 = ( 1.03 ) 4 − 1 = 0.1255 or 12 .55% For n = 12 . Substitute 0.12 for APR and 12 for n . APY= ( 1 + 0.12 12 ) 12 − 1 = ( 1.01 ) 12 − 1 = 0.1268 or 12 .68% For n = 365 . Substitute 0.12 for APR and 365 for n . APY= ( 1 + 0.12 365 ) 365 − 1 = ( 1.000328 ) 365 − 1 = 0.1274 or 12 .74% For n = 500 . Substitute 0.12 for APR and 500 for n . APY= ( 1 + 0.12 500 ) 500 − 1 = ( 1.00024 ) 500 − 1 = 0.127480 or 12 .75% For n = 1000 . Substitute 0.12 for APR and 1000 for n . APY= ( 1 + 0.12 1000 ) 1000 − 1 = ( 1.00012 ) 1000 − 1 = 0.127488 or 12 .75% Form a table of values of APY for different values of n . n APY 4 12.55 % 12 12.68 % 365 12.74 % 500 12.75 % 1000 12.75 % (b) The formula to calculate APY for given APR when interest is compounded annually is, APY=e r − 1 Where, ➣ r is the annual percentage rate (in decimal). Substitute 0...

6th Edition

ISBN: 9780137721023

Author: Bennett

Publisher: PEARSON C

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Chapter 4.B, Problem 102E

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The concept of continuous compounding and effect of continuous compounding as compared to other compounding and calculation of balance.

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Chapter 4.B, Problem 101E

Chapter 4.B, Problem 103E

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