A bank deposit paying simple interest at the rate of 8% per year grew to a sum of $1200 in 10 months. Find the principal. (Round your answer to the nearest cent.)
Simple interest is paid when the money is paid back (or in this case, withdrawn). That is not how banks compute interest either owed or paid, but since they want you to do it that way, here is what you do:
If the initial principal is X,
X*(1 + 0.08*(10/12)) = 1200.00
X*(1.06666667) = 1200
X = 1125.00
To find the principal, we can use the formula for simple interest:
Simple Interest = Principal x Rate x Time
Where:
Principal is the initial amount deposited,
Rate is the interest rate per year, and
Time is the time period in years.
Given that the bank deposit grew to $1200 in 10 months, we need to convert the time period to years.
10 months is equivalent to 10/12 = 5/6 years.
Now, we can set up the equation:
Simple Interest = Principal x Rate x Time
$1200 = Principal x 0.08 x (5/6)
To find the principal, divide both sides of the equation by (0.08 x 5/6):
Principal = $1200 / (0.08 x 5/6)
Principal = $1200 / (0.4/6)
Principal = $1200 x (6/0.4)
Principal = $1200 x 15
Principal = $18000
Therefore, the principal is $18,000.
To find the principal, we can use the formula for simple interest:
Simple Interest = (Principal * Interest Rate * Time)
First, let's convert the interest rate to a decimal: 8% = 0.08
Next, we need to convert the time from months to years. The given time is 10 months, so we divide by 12 to get 10/12 = 0.8333 years.
Now, we can plug the values into the formula and solve for the principal:
Simple Interest = (Principal * 0.08 * 0.8333)
$1200 = (Principal * 0.06664)
To isolate the principal, divide both sides of the equation by 0.06664:
Principal = $1200 / 0.06664
Principal ≈ $18005.40
Rounding to the nearest cent, the principal is approximately $18005.40.