When you purchase a home by securing a mortgage, the total paid toward the principal is your equity in the home. (Technically, the lending agency calculates your equity by subtracting the amount you still owe on your mortgage from the current value of your home, which may be higher or lower than your principal.) If your mortgage is for P dollars, and if the term of the mortgage is t months, then your equity E, in dollars, after k monthly payments is given below. E = P × (1 + r)k − 1 (1 + r)t − 1 Here r is the monthly interest rate as a decimal, with r = APR/12. Suppose you have a home mortgage of $396,000 for 30 years at an APR of 7%. (a) What is the monthly rate as a decimal? Round your answer to three decimal places. per month (b) Express, using functional notation, your equity after 20 years of payments. E( ) Calculate the value of the above term. (Round your answer to the nearest cent.) $ (c) Find a formula that gives your equity after y years of payments. (Use your rounded answer for the monthly rate.) E(y) =
Unitary Method
The word “unitary” comes from the word “unit”, which means a single and complete entity. In this method, we find the value of a unit product from the given number of products, and then we solve for the other number of products.
Speed, Time, and Distance
Imagine you and 3 of your friends are planning to go to the playground at 6 in the evening. Your house is one mile away from the playground and one of your friends named Jim must start at 5 pm to reach the playground by walk. The other two friends are 3 miles away.
Profit and Loss
The amount earned or lost on the sale of one or more items is referred to as the profit or loss on that item.
Units and Measurements
Measurements and comparisons are the foundation of science and engineering. We, therefore, need rules that tell us how things are measured and compared. For these measurements and comparisons, we perform certain experiments, and we will need the experiments to set up the devices.
When you purchase a home by securing a mortgage, the total paid toward the principal is your equity in the home. (Technically, the lending agency calculates your equity by subtracting the amount you still owe on your mortgage from the current value of your home, which may be higher or lower than your principal.) If your mortgage is for P dollars, and if the term of the mortgage is t months, then your equity E, in dollars, after k monthly payments is given below.
| (1 + r)k − 1 |
| (1 + r)t − 1 |
Here r is the monthly interest rate as a decimal, with r = APR/12.
Suppose you have a home mortgage of $396,000 for 30 years at an APR of 7%.
per month
(b) Express, using functional notation, your equity after 20 years of payments.
E( )
Calculate the value of the above term. (Round your answer to the nearest cent.)
$
(c) Find a formula that gives your equity after y years of payments. (Use your rounded answer for the monthly rate.)
E(y) =
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