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Michelle deposited a sum of money from a bank at an interest rate of 10% per year , compounded quarterly. If she earned an interest of $1375 in the second year, find the principal which she deposited.

 Oct 8, 2017
 #1
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Let the initial deposit that Michelle made = P

P x [1 + 0.10/4]^4

P x    1.025^4

=1.103812890625P  This is the balance of the deposit after the first year.

1.103812890625P + 1,375 = 1.103812890625^2P

1.103812890625P + 1,375 =1.21840289751P   Subtract 1.103812890625P from both sides.

1,375 =0.11459P      Divide both sides by 0.11459

P = 1,375 / 0.11459

P =11,999.30 - The initial principal that Michelle deposited in the Bank.

 Oct 8, 2017
 #2
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A simpler way of finding the initial deposit is as follows:

 

[1 + 0.10/4]^4 =1.103812890625 - 1 =0.103812890625 This is compounded  interest rate for 1 year.

$1,375 / 0.103812890625 =$13,244.98 - This is the balance after 1 year.

$13,244.98 / 1.103812890625

=$11,999.30 - The initial deposit made by Michelle.

 Oct 8, 2017

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