Albert Tilman wishes to buy a house selling for $90,000. His credit union requires him to make a 15% down payment. The current mortgage rate is 10.0%.
Find the required down payment and the total monthly payment for a 30-year loan.
Answer (2)
The required down payment is $13,500, and the total monthly payment for a 30-year loan at 10.0% interest rate is approximately $773.75.
To find the required down payment, we first calculate 15% of $90,000:
Down payment = 15% × $90 , 000 = 0.15 × $90 , 000 = $13 , 500
Albert Tilman needs to make a down payment of $13,500.
Next, to find the total monthly payment for a 30-year loan, we'll use the formula for the monthly payment on a fixed-rate mortgage:
M = P × ( 1 + r ) n − 1 r ( 1 + r ) n
Where:
M is the monthly payment
P is the principal loan amount (original loan amount minus down payment)
r is the monthly interest rate (annual rate divided by 12)
n is the number of payments (number of years times 12)
First, we calculate the monthly interest rate ( r ):
r = 12 × 100 10.0%
= 12 0.1
= 0.008333333
Now, we calculate the total number of payments ( n ):
n = 30 × 12
= 360
Substituting these values into the formula:
M = P × ( 1 + 0.008333333 ) 360 − 1 0.008333333 ( 1 + 0.008333333 ) 360 M = P × ( 1.008333333 ) 360 − 1 0.008333333 ( 1.008333333 ) 360
Since P = $90 , 000 − $13 , 500 = $76 , 500 , we plug this into the equation:
M = $76 , 500 × ( 1.008333333 ) 360 − 1 0.008333333 ( 1.008333333 ) 360
First, calculate (1.008333333)^{360} \
( 1.008333333 ) 360 ≈ 5.715578
Now, substitute this value back into the equation:
M = $76 , 500 × 5.715578 − 1 0.008333333 × 5.715578 M ≈ $76 , 500 × 4.715578 0.047630814 M ≈ $76 , 500 × 0.01011157 M ≈ $773.7477
So, the total monthly payment for a 30-year loan with a 10.0% mortgage rate is approximately $773.75.
Albert Tilman needs a down payment of $13,500 for a $90,000 house. His total monthly mortgage payment for a 30-year loan at a 10% interest rate is approximately $773.75.
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