Accumulated balance for simple interest

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helenli89

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Q:A fund earning 9% effective has a balance of $4,500 at the beginning of the year. If $500 is added to the fund at the end of three months and if $300 is withdrawn from the fund at the end of nine months, find the balance at the end of the year under the simple interest assumption.

My answer is: the total interest that will accumulate is 9%*4500 = 405. So 4500+500-300+405=5105.
But the correct answer is 5132. I don't understand how they get this answer.
Thanks.
 
helenli89 said:
Q:A fund earning 9% effective has a balance of $4,500 at the beginning of the year. If $500 is added to the fund at the end of three months and if $300 is withdrawn from the fund at the end of nine months, find the balance at the end of the year under the simple interest assumption.

My answer is: the total interest that will accumulate is 9%*4500 = 405. So 4500+500-300+405=5105.
But the correct answer is 5132. I don't understand how they get this answer.
Thanks.
Click to expand...

I have find the answer to my question. [(4500*(1.0072073^3)+500)*1.0072073^6 - 300]*1.0072073^3 = 5131.848963
But how come the quesiton asks "under the simple interest assumption", I don't understand why the question asks something about simple interest and the answer uses compounding interest mathod.
Thanks.
 
The exercise gives the "effective" rate, which is what you'd earn with simple interest, if the amount were allowed to sit, untouched, for the entire year. Since you are not given any information on the compounding period, and are instructed to use the simple-interest equivalent, just do that: use 9% simple interest.
 
helenli89 said:
My answer is: the total interest that will accumulate is 9%*4500 = 405. So 4500+500-300+405=5105.
Click to expand...
NO! 4500 is not each month's balance.

4500 for 3 months = 4500*.09 / 4 = 101.25 ; 500 is deposited:
5000 for 6 months = 5000*.09 / 2 = 225.00 ; 300 is withdrawn:
4700 for 3 months = 4700*.09 / 4 = 105.75
Add 'em up: 432.00

4700 + 432 = 5132

If you can't follow that, don't apply for a Bank job :wink:
 
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