Question

Calculate the equity each of these people has in his or her home: a. Fred just bought a house for \(\$ 200,000\) by putting \(10 \%\) as a down payment and borrowing the rest from the bank. b. Freda bought a house for \(\$ 150,000\) in cash, but if she were to sell it now, it would sell for \(\$ 250,000\). c. Frank bought a house for \(\$ 100,000\). He put \(20 \%\) down and borrowed the rest from the bank. However, the value of the house has now increased to \(\$ 160,000\) and he has paid off \(\$ 20,000\) of the bank loan.

Short answer

a. Fred's equity in his home is \$ 20,000. b. Freda's equity in her home is \$ 250,000. c. Frank's equity in his home is \$ 100,000.

Step-by-step solution

Case a: Calculate Down Payment

Fred put \(10 \%\) down on a house worth \(\$ 200,000\). To calculate the down payment, multiply the house value by the percentage. Down Payment = House Value * Down Payment Percentage Down Payment = \(\$200,000\) * \(10 \% = 0.10 \) Down Payment = \(\$20,000\)

Case a: Calculate Loan Amount

Fred borrowed the rest from the bank. To calculate the loan amount, subtract the down payment from the house value. Loan Amount = House Value - Down Payment Loan Amount = \(\$200,000 - \$20,000\) Loan Amount = \(\$180,000\)

Case a: Calculate Fred's Equity

Fred's equity is the difference between the current value of the house and the outstanding loan amount. Equity = House Value - Loan Amount Equity = \(\$200,000 - \$180,000\) Equity = \(\$20,000\)

Case b: Calculate Freda's Equity

Freda bought the house in cash and it is currently worth \(\$ 250,000\). Since there are no outstanding loans, her equity is equal to the current value of the house. Equity = Current Value of the House Equity = \(\$ 250,000\)

Case c: Calculate Down Payment

Frank put \(20 \%\) down on a house worth \(\$ 100,000\). To calculate the down payment, multiply the house value by the percentage. Down Payment = House Value * Down Payment Percentage Down Payment = \(\$100,000\) * \(20 \% = 0.20 \) Down Payment = \(\$20,000\)

Case c: Calculate Loan Amount Before Repayment

Frank borrowed the rest from the bank. To calculate the loan amount, subtract the down payment from the house value. Loan Amount = House Value - Down Payment Loan Amount = \(\$100,000 - \$20,000\) Loan Amount = \(\$80,000\)

Case c: Calculate Loan Amount After Repayment

Frank has paid off \(\$ 20,000\) of the loan. To calculate the current loan amount, subtract the paid amount from the initial loan amount. Current Loan Amount = Initial Loan Amount - Amount Paid Current Loan Amount = \(\$80,000 - \$20,000\) Current Loan Amount = \(\$60,000\)

Case c: Calculate Frank's Equity

Frank's equity is the difference between the current value of the house, which has increased to \(\$ 160,000\), and the outstanding loan amount after repayment. Equity = Current Value of the House - Outstanding Loan Amount Equity = \(\$ 160,000 - \$60,000\) Equity = \(\$ 100,000\) #Final Answer#: a. Fred's equity in his home is \$ 20,000. b. Freda's equity in her home is \$ 250,000. c. Frank's equity in his home is \$ 100,000.

Key concepts

Down Payment

The down payment on a home purchase represents the initial amount a buyer pays to reduce the loan amount financed by the lender. It's a critical factor in the home buying process, as it can affect loan approval, interest rates, and monthly mortgage payments.

Typically expressed as a percentage of the total property value, the down payment reduces the overall amount borrowed, which in turn decreases the financial burden on the buyer over the lifetime of the loan. In our example exercise, Fred's 10% down payment and Frank's 20% down payment reflect a common range that buyers might contribute upfront when purchasing their homes.

A larger down payment may also help in avoiding private mortgage insurance (PMI), which lenders often require when the down payment is less than 20% of the home’s purchase price. Making sense of a down payment is fundamental to understanding one’s immediate financial commitment when investing in real estate.

Loan Amount

The loan amount is the total sum of money borrowed from a financial institution to purchase a home, minus the down payment. Lenders calculate the loan amount by subtracting the down payment from the property's sales price.

In rate and term refinancing, as in Frank's scenario, the property owner borrows a sum equal to or less than the home's current mortgage balance. Understanding the initial loan amount and any subsequent changes due to payments is vital for homeowners who aim to manage their finances effectively. It is crucial to keep in mind the loan amount's influence on the interest and principal portions of future mortgage payments.

Property Value Appreciation

Property value appreciation refers to the increase in the value of a home over time, which can significantly impact the owner's equity. Various factors including market trends, home improvements, and changes in the surrounding area can influence appreciation rates.

In our case study, Freda's significant property appreciation—from \(150,000 to \)250,000—boosted her equity without any mortgage considerations, showcasing the potential for substantial financial gain. Similarly, Frank benefits from his home’s increased value to $160,000, which enhances his equity position. Understanding appreciation is essential for homeowners considering selling their property or looking to leverage their home’s equity.

Financial Mathematics

Financial mathematics comes into play when calculating the various aspects of home ownership, including equity, which is the owner’s financial stake in the property. It's the difference between the property's current market value and the remaining loan balance.

The mathematical formulas provided in the step-by-step solutions demonstrate how equity is calculated for Fred, Freda, and Frank, highlighting the dynamic nature of home ownership and financing. By mastering these financial equations, individuals can make informed decisions about their investments and understand the impact of payments, interest rates, and market changes on their home equity.