Question

Multiply compounding period: Find the future value of a five year $100,000 investment that pays 8.75% and that has the following compounding periods , Quarterly,Monthly,daily,Continous

Answer 1

Solution :-

Interest Rate Compounding Quarterly = 8.75%

Therefore Effective Annual Interest Rate = ( 1 + 0.0875 / 4 )⁴ - 1 = 0.0904 = 9.04%

If Interest Rate Compounding Monthly = 8.75%

Therefore Effective Annual Interest Rate = ( 1 + 0.0875 / 30 )³⁰ - 1 = 0.0913 = 9.13%

If Interest Rate Compounding Daily = 8.75%

Therefore Effective Annual Interest Rate = ( 1 + 0.0875 / 365 )³⁶⁵ - 1 = 0.091432 = 9.1432%

If Interest Rate Compounding Continuously = 8.75%

Therefore Effective Annual Interest Rate = e ^0.0875 - 1 = 0.0914423 = 9.144%

Future Value of $1,00,000 after 5 years

Future value , If Compounding Quarterly = $100,000 * ( 1 + 0.090413 )⁵

= $100,000 * 1.54154

= $154,154.11

Future Value , If Compounding Monthly = $100,000 * ( 1 + 0.091303 )⁵

= $100,000 * 1.54784

= $154,784.24

Future Value , If Compounding Daily = $100,000 * ( 1 + 0.091432 )⁵

= $100,000 * 1.54869

= $154,869.40

Future Value , If Compounding Continuously = $100,000 * ( 1 + 0.914423 )⁵

= $100,000 * 1.54883

= $154,883.10

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