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.
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.
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.