1) Carmen borrowed $1,200 for three months at 10.5% interest. How much interest did she pay for the loan?
2)Zack deposited $1,200 in a savings account that paid 7.75% simple interest. What was the balance in his account at the beginning of the third year?
3)Dan and Dawn purchased a house for $69,500. They had to make a down payment of 20%. How much was the amount of the mortgage they obtained?
1. I = Po*r*t = 1200*(0.105/12)*3.
2. P = Po + Po*r*t.
P = 1200 + 1200*0.0775*2 =
3. 100%-20% = 80% financed.
Po = 0.80 * 69,500 =
1) To calculate the interest Carmen paid for the loan, we can use the formula:
Interest = Principal * Rate * Time
Given:
Principal (P) = $1,200
Rate (R) = 10.5% or 0.105
Time (T) = 3 months or 3/12 years
Plugging in the values into the formula:
Interest = $1,200 * 0.105 * 3/12
Interest = $31.50
Therefore, Carmen paid $31.50 in interest for the loan.
2) To find the balance in Zack's account at the beginning of the third year, we need to calculate the interest earned on the initial deposit of $1,200.
Interest = Principal * Rate * Time
Given:
Principal (P) = $1,200
Rate (R) = 7.75% or 0.0775
Time (T) = 2 years (since it's at the beginning of the third year)
Plugging in the values into the formula:
Interest = $1,200 * 0.0775 * 2
Interest = $186
To find the balance, we add the interest to the principal:
Balance = Principal + Interest
Balance = $1,200 + $186
Balance = $1,386
Therefore, the balance in Zack's account at the beginning of the third year is $1,386.
3) The amount of the mortgage obtained by Dan and Dawn can be calculated by subtracting the down payment from the purchase price of the house.
Given:
Purchase Price = $69,500
Down Payment = 20% of the purchase price
Down Payment = 20/100 * $69,500
Down Payment = $13,900
Amount of Mortgage = Purchase Price - Down Payment
Amount of Mortgage = $69,500 - $13,900
Amount of Mortgage = $55,600
Therefore, the amount of the mortgage Dan and Dawn obtained is $55,600.
1) To calculate the interest Carmen paid for the loan, we need to use the formula:
Interest = Principal * Rate * Time
where Principal is the amount borrowed, Rate is the interest rate, and Time is the duration of the loan in years.
In this case, Carmen borrowed $1,200 for three months, which is equivalent to 0.25 years. The interest rate is 10.5%.
Substituting the values into the formula, we get:
Interest = $1,200 * 0.105 * 0.25
Interest = $31.50
Therefore, Carmen paid $31.50 in interest for the loan.
2) To calculate the balance in Zack's account at the beginning of the third year, we need to use the formula for simple interest:
Balance = Principal + (Principal * Rate * Time)
In this case, Zack deposited $1,200 in a savings account, the interest rate is 7.75%, and we want to find the balance at the beginning of the third year, which is equivalent to a time period of 2 years.
Substituting the values into the formula, we get:
Balance = $1,200 + ($1,200 * 0.0775 * 2)
Balance = $1,200 + $186
Balance = $1,386
Therefore, the balance in Zack's account at the beginning of the third year is $1,386.
3) To calculate the amount of the mortgage Dan and Dawn obtained, we need to subtract the down payment from the total purchase price of the house.
In this case, the purchase price of the house is $69,500, and the down payment is 20% of the purchase price. To calculate the down payment, we multiply the purchase price by 20%:
Down Payment = $69,500 * 0.20
Down Payment = $13,900
The amount of the mortgage is then calculated by subtracting the down payment from the purchase price:
Mortgage Amount = $69,500 - $13,900
Mortgage Amount = $55,600
Therefore, the amount of the mortgage Dan and Dawn obtained is $55,600.