Franklin deposited $1,400 in a savings account that accrues simple interest at 6.75%. What is the balance in his account at the beginning of the third quarter?
assuming
(a) the deposit was made at the beginning of the 1st quarter
(b) the interest is credited quarterly
then after two quarters (the beginning of the third quarter), the balance is
1400(1+2*.0675/4) = 1447.25
To find the balance in Franklin's account at the beginning of the third quarter, we need to calculate the simple interest earned and add it to the initial deposit.
Step 1: Calculate the simple interest earned.
Simple interest = Principal (P) x Rate (R) x Time (T)
Given:
Principal (P) = $1,400
Rate (R) = 6.75% or 0.0675 (in decimal form)
Time (T) = 2 quarters (since we want the balance at the beginning of the third quarter)
Simple interest = $1,400 x 0.0675 x 2
Simple interest = $189
Step 2: Find the balance in the account.
Balance = Principal (P) + Simple Interest
Balance = $1,400 + $189
Balance = $1,589
Therefore, the balance in Franklin's account at the beginning of the third quarter is $1,589.
To find the balance in Franklin's account at the beginning of the third quarter, we need to calculate the interest earned on the initial deposit and add it to the original amount.
The formula to find the simple interest is:
Interest = (Principal * Rate * Time) / 100
Let's calculate the interest earned for the first two quarters using this formula.
Interest for one quarter = ($1,400 * 6.75 * 1) / 100
Interest for two quarters = 2 * Interest for one quarter
To find the balance at the beginning of the third quarter, we add the interest earned for two quarters to the initial deposit:
Balance in the account at the beginning of the third quarter = $1,400 + Interest for two quarters
Now, let's calculate the interest and then find the balance.
Interest for one quarter = ($1,400 * 6.75 * 1) / 100 = $94.50
Interest for two quarters = 2 * $94.50 = $189
Balance in the account at the beginning of the third quarter = $1,400 + $189 = $1,589
The balance in Franklin's account at the beginning of the third quarter is $1,589.