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On Ashley's 18th birthday, she receives a gift of $10000, the accumulated amount of an...

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topgun13 | Honors

Posted January 11, 2012 at 2:49 PM via web

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On Ashley's 18th birthday, she receives a gift of $10000, the accumulated amount of an investment her grandfather made for her when she was born.

Determine the amount of the investment if the interest rate was 6.75% compounded: annually, semi-annually and monthly.

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justaguide | College Teacher | (Level 2) Distinguished Educator

Posted January 11, 2012 at 3:23 PM (Answer #1)

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Assume Ashley's grandfather invested an amount A when she was born. On her 18th birthday she receives $10000.

The annual rate of interest on the amount invested is 6.75%.

This gives:

For compounding done annually

10000 = A*(1.0675)^18

=> A = `10000/1.0675^18`

=> A = $ 3085.87

For compounding done semiannually

A = `10000/1.03375^36`

=> A= $ 3027.2

For compounding done monthly

A = `10000/(1.005625)^216`

=> A = $2977.21

The amount invested initially was $ 3085.87 for annual compounding, $3027.2 for semi-annual compounding and $2977.21 for monthly compounding.

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