Math Flashcards
Amortization Factor
Amortization Factor = [Monthly Interest Rate x (1+ Monthly Interest Rate)Number of Payments] / [(1+ Monthly Interest Rate)Number of Payments – 1]
Or we can write it a little more simply like this:
AF = [i x (1+ i)N] / [(1+ i)N – 1]
Where:
AF is the amortization factor
i is the monthly interest
N is the number of monthly payments made over the life of the mortgage.
A property owner has a 30-year mortgage with an 8% interest rate.
figure out the amortization factor
AF = [i x (1+ i)N] / [(1+ i)N – 1] x 1,000
7.338
Monthly Installment Payments
Monthly Payment = Principal x ([Monthly Interest Rate(1 + Monthly Interest Rate)Number of Payments] / [(1 + Monthly Interest Rate)Number of Payments -1])
Or
Monthly Payment = Principal x Amortization Factor
Or we can write it a little more simply like this:
MP = Pr x ([i x (1+ i)N] / [(1+ i)N – 1])
Where:
MP is the monthly payment
Pr is the principal
i is the monthly interest
N is the number of monthly payments made over the life of the mortgage
[i x (1+ i)N] / [(1+ i)N – 1] is the amortization factor
A property owner has a 15-year mortgage worth $120,000. The annual interest rate is 12%.
To figure out the amount of money the property owner pays each month we use the formula.
Monthly Payment = Principal x Amortization Factor
Or
MP = Pr x ([i x (1+ i)N] / [(1+ i)N – 1])
$1,428 = Monthly Payment
A property owner pays $2,562.50 a month on a 40-year mortgage with a 4% interest rate.
We will need to use the monthly payment formula to figure out the principal amount of the loan.
Monthly Payment = Principal x Amortization Factor
Or
MP = Pr x ([i x (1+ i)N] / [(1+ i)N – 1])
The principal of the mortgage is $625,000.
A property owner pays $2,562.50 a month on a 40-year mortgage with a 4% interest rate.
We will need to use the monthly payment formula to figure out the principal amount of the loan.
Monthly Payment = Principal x Amortization Factor
Or
MP = Pr x ([i x (1+ i)N] / [(1+ i)N – 1])
The principal of the mortgage is $625,000.
Loan Discount Points
Discount points are a method offered by lenders to allow borrowers a way to lower the interest rate. Most often, one discount point lowers the interest rate by 1/8th for a cost equal to 1% of the principal.
There is a property owner who is borrowing $80,000 to build an addition to a house. Unfortunately, the 9.75% interest rate is a little high for the property owner. She decides to “buy” 10 discount points.
To figure out the degree to which the interest would be lowered we need to use the following formula.
Interest rate - (Number of Points x 1/8) = Adjusted Interest Rate
To determine the cost of the discount points we need to use a formula that looks like this:
(Loan Amount x .01) x Number of points = Cost of Discount Points
The property owner now has an 8.5% interest rate but she had to spend $8,000 to get that new rate.
Just to put that in context, if the length of the mortgage is 30 years, an 8.5% rate compared to 9.75% would lower the monthly payment from $687.32 to $629.36, amounting to a savings of nearly $21,000 over the life of the loan.
Total Cost of the Loan
The total cost of a loan is the total amount of money a borrower will pay back to the lender. It is found by adding the original amount of loaned money (the principal) to the amount of money in interest that accrues over the life of the mortgage.
There are a couple of formulas for determining the total cost of the loan. The first method uses the amortized mortgage payments. That formula looks like this:
Total Cost of a Loan = Amortized Mortgage Payment x Number of Payments
The other formula for determining the total cost of a loan looks like this:
Total Cost of a Loan = Principal + Paid Interest
find the total cost of the loan
A property owner makes amortized monthly payments of $7,625 on a 30-year mortgage.
$2,745,000
